Question

question 15 1 pts the distance between the southeast corner of section 4 and the northwest corner of section 34 in a given township is: 8 miles 4 miles 10 miles 12 miles question 16 1 pts in what direction does the humboldt meridian line run? northwest north and south east and west southwest

Explanation:

Question 15

Step1: Recall Township/Section Layout

A township is divided into 36 sections (6x6 grid), each section is 1 square mile (1 mile x 1 mile). Section numbering: starts at NE corner (section 1), goes right (east) to section 6, then down (south) a row, left (west) to section 7, etc. So section 4 is in the top - left part (row 1, column 4), section 34: let's find its position. The 6th row (bottom row) of sections: section 31 (NE of 6th row), 32, 33, 34 (SW of 6th row).

Step2: Calculate Distance in Miles

• Horizontal (east - west) distance: Section 4 is in column 4 (from west, column 1 is east - most? Wait, no: section 1 is NE (column 1, row 1), section 6 is SE (column 6, row 1). Then row 2: section 7 (NW, column 1, row 2), section 12 (SW, column 6, row 2). So for row 1 (top row), sections 1 - 6 (east - west, row 1). Row 2: 7 - 12 (row 2, west - east? Wait, no, the numbering is serpentine: row 1 (north row): sections 1 (NE), 2, 3, 4, 5, 6 (SE). Row 2 (next south): sections 7 (NW), 8, 9, 10, 11, 12 (SW). Row 3: 13 (NE), 14, 15, 16, 17, 18 (SE). Row 4: 19 (NW), 20, 21, 22, 23, 24 (SW). Row 5: 25 (NE), 26, 27, 28, 29, 30 (SE). Row 6 (south row): 31 (NW), 32, 33, 34 (SW).

• So section 4: row 1, column 4 (east - west: column 4, row 1 (north - south: row 1)). Section 34: row 6, column 4 (wait, no: row 6, sections 31 (column 1), 32 (2), 33 (3), 34 (4)? Wait, no, serpentine: row 1 (north): 1 (col1) - 6 (col6) (east - west). Row 2: 7 (col6) - 12 (col1) (west - east). Row 3: 13 (col1) - 18 (col6) (east - west). Row 4: 19 (col6) - 24 (col1) (west - east). Row 5: 25 (col1) - 30 (col6) (east - west). Row 6: 31 (col6) - 34 (col3)? Wait, I think I messed up. Let's use the standard: each township is 6 miles square (6 miles north - south, 6 miles east - west), divided into 36 sections, each 1 mile square. The section numbering: starts at NE corner (section 1), then east to section 6 (SE corner of township), then south 1 mile (row 2), west to section 7 (NW corner of row 2), then east to section 12 (SW corner of row 2), then south 1 mile (row 3), east to section 13 (NE corner of row 3), etc. So:

• Row 1 (north - most, 1 mile south of township's north boundary): sections 1 (NE, x = 0 - 1, y = 5 - 6), 2 (x = 1 - 2, y = 5 - 6), 3 (x = 2 - 3, y = 5 - 6), 4 (x = 3 - 4, y = 5 - 6), 5 (x = 4 - 5, y = 5 - 6), 6 (x = 5 - 6, y = 5 - 6) (y - axis: north is higher, from 0 (south) to 6 (north)).

• Row 2 (1 - 2 miles south of north boundary): sections 7 (x = 5 - 6, y = 4 - 5), 8 (x = 4 - 5, y = 4 - 5), 9 (x = 3 - 4, y = 4 - 5), 10 (x = 2 - 3, y = 4 - 5), 11 (x = 1 - 2, y = 4 - 5), 12 (x = 0 - 1, y = 4 - 5)

• Row 3 (2 - 3 miles south): sections 13 (x = 0 - 1, y = 3 - 4), 14 (x = 1 - 2, y = 3 - 4), 15 (x = 2 - 3, y = 3 - 4), 16 (x = 3 - 4, y = 3 - 4), 17 (x = 4 - 5, y = 3 - 4), 18 (x = 5 - 6, y = 3 - 4)

• Row 4 (3 - 4 miles south): sections 19 (x = 5 - 6, y = 2 - 3), 20 (x = 4 - 5, y = 2 - 3), 21 (x = 3 - 4, y = 2 - 3), 22 (x = 2 - 3, y = 2 - 3), 23 (x = 1 - 2, y = 2 - 3), 24 (x = 0 - 1, y = 2 - 3)

• Row 5 (4 - 5 miles south): sections 25 (x = 0 - 1, y = 1 - 2), 26 (x = 1 - 2, y = 1 - 2), 27 (x = 2 - 3, y = 1 - 2), 28 (x = 3 - 4, y = 1 - 2), 29 (x = 4 - 5, y = 1 - 2), 30 (x = 5 - 6, y = 1 - 2)

• Row 6 (5 - 6 miles south, south - most row): sections 31 (x = 5 - 6, y = 0 - 1), 32 (x = 4 - 5, y = 0 - 1), 33 (x = 3 - 4, y = 0 - 1), 34 (x = 2 - 3, y = 0 - 1)

Now, Southeast corner of section 4: section 4 has x from 3 - 4, y from 5 - 6. Southeast corner is (4, 5) (x = 4, y = 5).

Northwest corner of section 34: section 34 has x from 2 - 3, y from 0 - 1. Northwest corn…

Answer:

Step1: Recall Township/Section Layout

A township is divided into 36 sections (6x6 grid), each section is 1 square mile (1 mile x 1 mile). Section numbering: starts at NE corner (section 1), goes right (east) to section 6, then down (south) a row, left (west) to section 7, etc. So section 4 is in the top - left part (row 1, column 4), section 34: let's find its position. The 6th row (bottom row) of sections: section 31 (NE of 6th row), 32, 33, 34 (SW of 6th row).

Step2: Calculate Distance in Miles

• Horizontal (east - west) distance: Section 4 is in column 4 (from west, column 1 is east - most? Wait, no: section 1 is NE (column 1, row 1), section 6 is SE (column 6, row 1). Then row 2: section 7 (NW, column 1, row 2), section 12 (SW, column 6, row 2). So for row 1 (top row), sections 1 - 6 (east - west, row 1). Row 2: 7 - 12 (row 2, west - east? Wait, no, the numbering is serpentine: row 1 (north row): sections 1 (NE), 2, 3, 4, 5, 6 (SE). Row 2 (next south): sections 7 (NW), 8, 9, 10, 11, 12 (SW). Row 3: 13 (NE), 14, 15, 16, 17, 18 (SE). Row 4: 19 (NW), 20, 21, 22, 23, 24 (SW). Row 5: 25 (NE), 26, 27, 28, 29, 30 (SE). Row 6 (south row): 31 (NW), 32, 33, 34 (SW).

• So section 4: row 1, column 4 (east - west: column 4, row 1 (north - south: row 1)). Section 34: row 6, column 4 (wait, no: row 6, sections 31 (column 1), 32 (2), 33 (3), 34 (4)? Wait, no, serpentine: row 1 (north): 1 (col1) - 6 (col6) (east - west). Row 2: 7 (col6) - 12 (col1) (west - east). Row 3: 13 (col1) - 18 (col6) (east - west). Row 4: 19 (col6) - 24 (col1) (west - east). Row 5: 25 (col1) - 30 (col6) (east - west). Row 6: 31 (col6) - 34 (col3)? Wait, I think I messed up. Let's use the standard: each township is 6 miles square (6 miles north - south, 6 miles east - west), divided into 36 sections, each 1 mile square. The section numbering: starts at NE corner (section 1), then east to section 6 (SE corner of township), then south 1 mile (row 2), west to section 7 (NW corner of row 2), then east to section 12 (SW corner of row 2), then south 1 mile (row 3), east to section 13 (NE corner of row 3), etc. So:

• Row 1 (north - most, 1 mile south of township's north boundary): sections 1 (NE, x = 0 - 1, y = 5 - 6), 2 (x = 1 - 2, y = 5 - 6), 3 (x = 2 - 3, y = 5 - 6), 4 (x = 3 - 4, y = 5 - 6), 5 (x = 4 - 5, y = 5 - 6), 6 (x = 5 - 6, y = 5 - 6) (y - axis: north is higher, from 0 (south) to 6 (north)).

• Row 2 (1 - 2 miles south of north boundary): sections 7 (x = 5 - 6, y = 4 - 5), 8 (x = 4 - 5, y = 4 - 5), 9 (x = 3 - 4, y = 4 - 5), 10 (x = 2 - 3, y = 4 - 5), 11 (x = 1 - 2, y = 4 - 5), 12 (x = 0 - 1, y = 4 - 5)

• Row 3 (2 - 3 miles south): sections 13 (x = 0 - 1, y = 3 - 4), 14 (x = 1 - 2, y = 3 - 4), 15 (x = 2 - 3, y = 3 - 4), 16 (x = 3 - 4, y = 3 - 4), 17 (x = 4 - 5, y = 3 - 4), 18 (x = 5 - 6, y = 3 - 4)

• Row 4 (3 - 4 miles south): sections 19 (x = 5 - 6, y = 2 - 3), 20 (x = 4 - 5, y = 2 - 3), 21 (x = 3 - 4, y = 2 - 3), 22 (x = 2 - 3, y = 2 - 3), 23 (x = 1 - 2, y = 2 - 3), 24 (x = 0 - 1, y = 2 - 3)

• Row 5 (4 - 5 miles south): sections 25 (x = 0 - 1, y = 1 - 2), 26 (x = 1 - 2, y = 1 - 2), 27 (x = 2 - 3, y = 1 - 2), 28 (x = 3 - 4, y = 1 - 2), 29 (x = 4 - 5, y = 1 - 2), 30 (x = 5 - 6, y = 1 - 2)

• Row 6 (5 - 6 miles south, south - most row): sections 31 (x = 5 - 6, y = 0 - 1), 32 (x = 4 - 5, y = 0 - 1), 33 (x = 3 - 4, y = 0 - 1), 34 (x = 2 - 3, y = 0 - 1)

Now, Southeast corner of section 4: section 4 has x from 3 - 4, y from 5 - 6. Southeast corner is (4, 5) (x = 4, y = 5).

Northwest corner of section 34: section 34 has x from 2 - 3, y from 0 - 1. Northwest corner is (2, 1) (x = 2, y = 1). Wait, no, coordinates: x is east - west (0 at west, 6 at east), y is north - south (0 at south, 6 at north). So northwest corner of a section: x = left boundary, y = top boundary. Section 34: x left = 2, x right = 3; y top = 1, y bottom = 0. So northwest corner is (2, 1). Southeast corner of section 4: x right = 4, y bottom = 5.

Now, calculate the distance. The north - south distance: from y = 5 (section 4's SE corner) to y = 1 (section 34's NW corner) is 5 - 1 = 4 miles. The east - west distance: from x = 4 (section 4's SE corner) to x = 2 (section 34's NW corner) is 4 - 2 = 2 miles. Wait, that can't be. Wait, maybe I messed up the section numbering. Let's use another approach: each township is 6 miles square. Sections are numbered such that section 1 is NE, section 36 is SW. Wait, no, standard is 36 sections, 6x6, section 1 NE, section 6 SE, section 7 SW of row 2, section 12 NW of row 2? No, I think the correct way is that in a township (6 miles x 6 miles), each section is 1 mile x 1 mile. The distance between section 4 and section 34: let's find how many sections apart they are in north - south and east - west.

Section 4: in the first row (north - most row, row 1: sections 1 - 6). Section 34: let's see, row 1: 1 - 6, row 2: 7 - 12, row 3: 13 - 18, row 4: 19 - 24, row 5: 25 - 30, row 6: 31 - 36? Wait, I had a mistake earlier, section 36 is SW, not 34. Oh! That's the error. So row 6 (south - most row) has sections 31 (NW of row 6), 32, 33, 34, 35, 36 (SE of row 6). So section 34 is in row 6, column 4 (if row 1: columns 1 - 6 (1 - 6), row 2: columns 6 - 1 (7 - 12), row 3: columns 1 - 6 (13 - 18), row 4: columns 6 - 1 (19 - 24), row 5: columns 1 - 6 (25 - 30), row 6: columns 1 - 6 (31 - 36)). Wait, no, serpentine numbering: row 1 (north): 1 (col1) - 6 (col6) (east - west). Row 2 (south of row 1): 7 (col6) - 12 (col1) (west - east). Row 3 (south of row 2): 13 (col1) - 18 (col6) (east - west). Row 4 (south of row 3): 19 (col6) - 24 (col1) (west - east). Row 5 (south of row 4): 25 (col1) - 30 (col6) (east - west). Row 6 (south of row 5): 31 (col6) - 36 (col1) (west - east). Ah! So section 34: row 6, col3 (since 31 (col6), 32 (col5), 33 (col4), 34 (col3), 35 (col2), 36 (col1)). Section 4: row 1, col4 (col1 - 6, row 1).

Now, coordinates: x (east - west, 0 at west, 6 at east), y (north - south, 0 at south, 6 at north).

Section 4 (row 1, col4): x from 3 - 4 (col4: 3 ≤ x < 4), y from 5 - 6 (row 1: 5 ≤ y < 6). Southeast corner: (4, 5).

Section 34 (row 6, col3): x from 2 - 3 (col3: 2 ≤ x < 3), y from 0 - 1 (row 6: 0 ≤ y < 1). Northwest corner: (2, 1).

Now, north - south distance: 5 - 1 = 4 miles (since y decreases southward, from y = 5 to y = 1 is 4 miles south). East - west distance: 4 - 2 = 2 miles (x decreases westward, from x = 4 to x = 2 is 2 miles west). Wait, but the answer options are 8,4,10,12. So my coordinate system is wrong. Let's use the fact that a township is 6 miles on each side. The distance between section 4 and section 34: let's find the number of miles north - south and east - west.

Section 4: in the first row (top row), so its north - south position is 5 - 6 miles from the south (or 0 - 1 miles from the north). Section 34: in the sixth row (bottom row), 0 - 1 miles from the south. Wait, no, row 1 is north - most (1 mile south of township's north edge), row 6 is south - most (1 mile north of township's south edge). So the north - south distance between row 1 and row 6 is 6 - 2 = 4 miles (since each row is 1 mile tall, 6 rows, but from row 1 (y = 5 - 6) to row 6 (y = 0 - 1), the vertical distance is 5 - 0 = 5? No, I'm confused. Let's use the standard formula: in a township, the distance between section A and section B:

• First, find the township's section grid: 6 sections east - west (6 miles) and 6 sections north - south (6 miles).

• Section numbering: starts at NE (section 1), goes east to section 6 (SE), then south 1 mile, west to section 7 (NW of row 2), east to section 12 (SW of row 2), south 1 mile, east to section 13 (NE of row 3), etc.

So section 4: row 1 (north row), column 4 (east - west, column 4: 3 - 4 miles from west, 2 - 3 miles from east).

Section 34: let's count the rows from north: row 1 (1 - 6), row 2 (7 - 12), row 3 (13 - 18), row 4 (19 - 24), row 5 (25 - 30), row 6 (31 - 36). So section 34 is in row 6, column 3 (since 31 (col6), 32 (col5), 33 (col4), 34 (col3), 35 (col2), 36 (col1)).

Now, the north - south distance between row 1 and row 6: 6 - 1 = 5 miles? No, each row is 1 mile, so from row 1 (top) to row 6 (bottom) is 5 miles? But the answer options have 4. Wait, maybe the section numbering is different. Let's think of the township as 36 sections, 6x6, with section 1 at NE, section 36 at SW. The distance between section 4 (row 1, column 4) and section 34 (row 6, column 4) would be 5 miles, but that's not an option. Wait, maybe the question is about a different section numbering. Wait, another approach: in a township, the distance between the SE corner of section 4 and NW corner of section 34.

SE corner of section 4: section 4 is in the first tier (north - south) and fourth range (east - west). SE corner: range 4, tier 1 (SE corner of tier 1, range 4).

NW corner of section 34: section 34 is in the sixth tier (south - north) and fourth range? Wait, no, maybe the ranges and tiers. A township has 6 ranges (east - west) and 6 tiers (north - south), each 1 mile.

Section 4: range 4, tier 1 (tier 1 is north - most, range 4 is 4th east - west).

Section 34: let's calculate the tier and range. Section number = (tier - 1)6 + range (if tier is odd) or section number = (tier - 1)6 + (7 - range) (if tier is even). Wait, for tier 1 (odd): section 1 = (1 - 1)6 + 1 = 1, section 6 = (1 - 1)6 + 6 = 6. Tier 2 (even): section 7 = (2 - 1)*6 + (7 - 1)=6 + 6 = 12? No, that's not right. Wait, the correct formula for section number in serpentine numbering:

For tier \( t \) (1 = north - most, 6 = south - most):

• If \( t \) is odd: section number \( s = (t - 1)*6 + r \), where \( r = 1,2,3,4,5,6 \) (east - west range, 1 = east - most, 6 = west - most? No, confusion between east and west. Let's define range as east - west, range 1 = west - most, range 6 = east - most