Question

question 15
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
in what direction does the humboldt meridian line run?
northwest
north and south
east and west
southwest

Explanation:

Question 15

Step1: Recall township and section layout

A township is divided into 36 sections, arranged in a 6x6 grid. Each section is 1 mile square. Sections are numbered from 1 (northeast) to 36 (southeast) in a township. Section 4 is in the upper (north) part, section 34 is in the lower (south) part. The vertical (north - south) distance between their corners: from section 4 (north) to section 34 (south), the number of sections between them vertically: section 4 is in row 1 (top row of 6), section 34 is in row 6 (bottom row). The vertical distance between rows: each section is 1 mile, so from row 1 to row 6, the number of miles north - south is \(6 - 1= 5\)? Wait, no, wait. Wait, the township is 6 miles by 6 miles (36 sections, each 1 mile). Wait, section numbering: section 1 is NE, section 6 is NW of top row; section 7 is next row down, etc. Wait, actually, the distance between southeast corner of section 4 and northwest corner of section 34: let's think about the grid. Section 4: in a township, sections are numbered left - right, top - bottom? Wait, no, the standard section numbering is: starting at NE corner, section 1, then section 2 to 6 (left to right, top row). Then next row down (south), section 7 to 12, etc. So section 4 is in the top row (row 1, north), column 4 (west - east? Wait, no, section 1 is NE, so column 1 (east), row 1 (north). So section 4 would be column 4 (west), row 1 (north). Section 34: let's see, 36 sections, 6 rows (north - south) and 6 columns (east - west). Row 1: sections 1 - 6 (northmost), row 2: 7 - 12, row 3: 13 - 18, row 4: 19 - 24, row 5: 25 - 30, row 6: 31 - 36 (southmost). So section 34 is in row 6 (south), column 4 (since 31 is column 1, 32 column 2, 33 column 3, 34 column 4). So southeast corner of section 4: section 4 is row 1, column 4. Southeast corner is (column 4, row 1) - southeast, so (east - west: column 4, north - south: row 1, so southeast corner is (x = 4 miles east, y = 1 mile south? Wait, no, each section is 1 mile square. The township is 6 miles east - west and 6 miles north - south. So the coordinates: let's set the NE corner of the township as (0,6) (x: east - west, y: north - south). Then section 1: NE corner (0,6), SE corner (1,6), SW corner (1,5), NW corner (0,5). Section 2: NE (1,6), SE (2,6), SW (2,5), NW (1,5).... Section 6: NE (5,6), SE (6,6), SW (6,5), NW (5,5). Then row 2 (next south): section 7: NE (0,5), SE (1,5), SW (1,4), NW (0,4).... Section 12: NE (5,5), SE (6,5), SW (6,4), NW (5,4). Row 3: 13 - 18 (y from 4 to 3), row 4: 19 - 24 (y from 3 to 2), row 5: 25 - 30 (y from 2 to 1), row 6: 31 - 36 (y from 1 to 0). So section 34: row 6, column 4. So column 4: x from 3 to 4 (since column 1: 0 - 1, column 2:1 - 2, column 3:2 - 3, column 4:3 - 4, column 5:4 - 5, column 6:5 - 6). Row 6: y from 0 to 1 (since row 1: y 5 - 6, row 2:4 - 5, row 3:3 - 4, row 4:2 - 3, row 5:1 - 2, row 6:0 - 1). So northwest corner of section 34: x = 3, y = 1 (since northwest corner is (x start of column 4, y end of row 6) = (3,1)). Southeast corner of section 4: section 4 is row 1, column 4. Row 1: y 5 - 6, column 4: x 3 - 4. Southeast corner is (x = 4, y = 5) (since southeast is (x end, y start of row? Wait, no, confusion. Let's re - define: for a section, NE corner is (x, y), SE is (x + 1, y), SW is (x + 1, y - 1), NW is (x, y - 1), where x is east - west, y is north - south. So section 4: row 1 (northmost row), column 4 (fourth column from east). So NE corner of section 4: x = 3 (since column 1: x 0 - 1, column 2:1 - 2, column 3:2 - 3, column 4:3 - 4), y = 6 (northmost y). So SE corner of section 4: x…

Meridian lines, by definition, run in the north - south direction. The Humboldt Meridian is a meridian line, so it runs north and south.

Answer:

8 miles

Question 16