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use the diagram. (section 1.1) 1. name four points. 2. name three colli…

Question

use the diagram. (section 1.1)

  1. name four points.
  2. name three collinear points.
  3. name two lines.
  4. name three coplanar points.
  5. name the plane that is shaded green.
  6. give two names for the plane that is shaded blue.
  7. name three line - segments.
  8. name three rays.

sketch the figure described. (section 1.1)

  1. $overline{qr}$ and $overline{qs}$
  2. plane $p$ intersecting $overleftrightarrow{yz}$ at $z$

plot the points in a coordinate plane. then determine whether $overline{ab}$ and $overline{cd}$ are congruent. (section 1.2)

  1. $a(-3,3),b(1,3),c(3,2),d(3, - 2)$
  2. $a(-8,7),b(1,7),c(-3, - 6),d(5, - 6)$

find $ac$. (section 1.2)

  1. $a$ 13 $b$ 26 $c$
  2. $a$ 62 $c$ 11 $b$

find the coordinates of the mid - point $m$ and the distance between the two points. (section 1.3)

  1. $j(4,3)$ and $k(2, - 3)$
  2. $l(-4,5)$ and $n(5, - 3)$
  3. $p(-6, - 1)$ and $q(1,2)$
  4. identify the segment bisector of $overline{rs}$. then find $rs$. (section 1.3)

$r$ $6x - 2$ $m$ $3x + 7$ $s$

  1. the mid - point of $overline{jk}$ is $m(0,1)$. one endpoint is $j(-6,3)$. find the coordinates of endpoint $k$. (section 1.3)
  2. your mom asks you to run some errands on your way home from school. she wants you to stop at the post office and the grocery store, which are both on the same straight road between your school and your house. the distance from your school to the post office is 376 yards, the distance from the post office to your house is 929 yards, and the distance from the grocery store to your house is 513 yards. (section 1.2)

a. where should you stop first?
b. what is the distance from the post office to the grocery store?
c. what is the distance from your school to your house?
d. you walk at a speed of 75 yards per minute. how long does it take you to walk straight home from school? explain your answer.

  1. the figure shows a coordinate plane on a baseball field. the distance from home plate to first base is 90 feet. the pitching mound is the mid - point between home plate and second base. find the distance from home plate

Explanation:

Step1: Answer question 1

Points can be named as A, B, C, D (any 4 from the diagram).

Step2: Answer question 2

Collinear points lie on the same line. For example, B, C, D are collinear.

Step3: Answer question 3

Lines can be named as $\overleftrightarrow{BC}$ and $\overleftrightarrow{AB}$ (any 2 from the diagram).

Step4: Answer question 4

Coplanar points lie on the same plane. A, B, C are coplanar (any 3 in the same - plane from the diagram).

Step5: Answer question 5

The shaded - green plane can be named as plane FGH.

Step6: Answer question 6

The shaded - blue plane can be named as plane ABCD or plane ABE.

Step7: Answer question 7

Line segments can be named as $\overline{AB}$, $\overline{BC}$, $\overline{CD}$.

Step8: Answer question 8

Rays can be named as $\overrightarrow{AB}$, $\overrightarrow{BC}$, $\overrightarrow{CD}$.

Step9: Answer question 9

Sketch two rays $\overrightarrow{QR}$ and $\overrightarrow{QS}$ with a common endpoint Q.

Step10: Answer question 10

Sketch a plane P intersecting a line $\overleftrightarrow{YZ}$ at point Z.

Step11: Answer question 11

For points $A(-3,3)$, $B(1,3)$, $C(3,2)$, $D(3, - 2)$:
The length of $\overline{AB}=\vert1-( - 3)\vert=4$ (using the distance formula for horizontal line $d=\vert x_2 - x_1\vert$ as $y$ - coordinates are the same).
The length of $\overline{CD}=\vert2-( - 2)\vert = 4$ (using the distance formula for vertical line $d=\vert y_2 - y_1\vert$ as $x$ - coordinates are the same). So, $\overline{AB}$ and $\overline{CD}$ are congruent.

Step12: Answer question 12

For points $A(-8,7)$, $B(1,7)$, $C(-3,-6)$, $D(5,-6)$:
The length of $\overline{AB}=\vert1-( - 8)\vert = 9$ (using the distance formula for horizontal line $d=\vert x_2 - x_1\vert$ as $y$ - coordinates are the same).
The length of $\overline{CD}=\vert5-( - 3)\vert=8$ (using the distance formula for horizontal line $d=\vert x_2 - x_1\vert$ as $y$ - coordinates are the same). So, $\overline{AB}$ and $\overline{CD}$ are not congruent.

Step13: Answer question 13

If $AB = 13$ and $BC = 26$, then $AC=AB + BC=13 + 26=39$.

Step14: Answer question 14

If $AB = 62$ and $BC = 11$, then $AC=AB - BC=62-11 = 51$.

Step15: Answer question 15

For points $J(4,3)$ and $K(2,-3)$:
The mid - point formula is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
$M(\frac{4 + 2}{2},\frac{3+( - 3)}{2})=M(3,0)$.
The distance formula is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
$d=\sqrt{(2 - 4)^2+( - 3 - 3)^2}=\sqrt{(-2)^2+( - 6)^2}=\sqrt{4 + 36}=\sqrt{40}=2\sqrt{10}$.

Step16: Answer question 16

For points $L(-4,5)$ and $N(5,-3)$:
$M(\frac{-4 + 5}{2},\frac{5+( - 3)}{2})=M(\frac{1}{2},1)$.
$d=\sqrt{(5-( - 4))^2+( - 3 - 5)^2}=\sqrt{(9)^2+( - 8)^2}=\sqrt{81 + 64}=\sqrt{145}$.

Step17: Answer question 17

For points $P(-6,-1)$ and $Q(1,2)$:
$M(\frac{-6 + 1}{2},\frac{-1+2}{2})=M(-\frac{5}{2},\frac{1}{2})$.
$d=\sqrt{(1-( - 6))^2+(2-( - 1))^2}=\sqrt{(7)^2+(3)^2}=\sqrt{49 + 9}=\sqrt{58}$.

Step18: Answer question 18

Since $M$ is the mid - point of $\overline{RS}$, then $6x-2=3x + 7$.
$6x-3x=7 + 2$, $3x=9$, $x = 3$.
$RS=(6x-2)+(3x + 7)=6\times3-2+3\times3 + 7=18-2+9 + 7=32$. The segment bisector is point M.

Step19: Answer question 19

Let the coordinates of $K$ be $(x,y)$.
Using the mid - point formula: $\frac{-6 + x}{2}=0$ and $\frac{3 + y}{2}=1$.
From $\frac{-6 + x}{2}=0$, we get $-6+x = 0$, $x = 6$.
From $\frac{3 + y}{2}=1$, we get $3 + y=2$, $y=-1$. So, $K(6,-1)$.

Step20: Answer question 20a

The post - office is closer to the school. So, stop at the post - office first.

Step20: Answer question 20b

The distance fro…

Answer:

  1. A, B, C, D
  2. B, C, D
  3. $\overleftrightarrow{BC}$, $\overleftrightarrow{AB}$
  4. A, B, C
  5. plane FGH
  6. plane ABCD, plane ABE
  7. $\overline{AB}$, $\overline{BC}$, $\overline{CD}$
  8. $\overrightarrow{AB}$, $\overrightarrow{BC}$, $\overrightarrow{CD}$
  9. Sketch two rays $\overrightarrow{QR}$ and $\overrightarrow{QS}$ with a common endpoint Q.
  10. Sketch a plane P intersecting a line $\overleftrightarrow{YZ}$ at point Z.
  11. $\overline{AB}$ and $\overline{CD}$ are congruent.
  12. $\overline{AB}$ and $\overline{CD}$ are not congruent.
  13. 39
  14. 51
  15. Mid - point $M(3,0)$, Distance $2\sqrt{10}$
  16. Mid - point $M(\frac{1}{2},1)$, Distance $\sqrt{145}$
  17. Mid - point $M(-\frac{5}{2},\frac{1}{2})$, Distance $\sqrt{58}$
  18. Segment bisector is point M, $RS = 32$
  19. $K(6,-1)$

20a. Post - office
20b. 416 yards
20c. 1305 yards
20d. 17.4 minutes

  1. Approximately 63.6 feet