Question

1. use the diagram below to answer the questions to the right.
2. find the midpoint between the following points: (-3, 5) and (1, 8)
3. one endpoint of a segment is located at (2, 7). the midpoint is located at (-1, 10). find the other endpoint.
4. find the distance between the following two points: (5, -1) and (-3, 7)
5. a delivery drone flies from warehouse a located at coordinates a(2, 3) to a customers location at point b(10, 11) on a coordinate grid representing a city map.

a) find midpoint m of the segment ab. what does the midpoint represent in the context of the drones flight?
b) calculate the distance between points a and b. what does this distance represent in the real world?

Explanation:

6a)

Identify a line on Plane T.
Line BD lies on Plane T.

6b)

Find a line with Point D.
Line BD contains Point D.

6c)

Find three collinear points.
Points B, C, and D are collinear.

6d)

Find four coplanar points.
Points A, B, C, and N are coplanar (lying on the rectangular - shaped plane).

6e)

Find a pair of opposite rays.
Rays CB and CD are opposite rays.

7)

Use mid - point formula $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
Let $(x_1,y_1)=(-3,5)$ and $(x_2,y_2)=(1,8)$.
$x=\frac{-3 + 1}{2}=\frac{-2}{2}=-1$
$y=\frac{5 + 8}{2}=\frac{13}{2}=6.5$
Mid - point is $(-1,6.5)$

8)

Let the endpoints be $(x_1,y_1)=(2,7)$ and mid - point $(x_m,y_m)=(-1,10)$. Let the other endpoint be $(x_2,y_2)$.
Use mid - point formula $x_m=\frac{x_1 + x_2}{2}$ and $y_m=\frac{y_1 + y_2}{2}$.
For x - coordinate: $-1=\frac{2 + x_2}{2}$, then $-2=2 + x_2$, $x_2=-4$.
For y - coordinate: $10=\frac{7 + y_2}{2}$, then $20=7 + y_2$, $y_2 = 13$.
The other endpoint is $(-4,13)$

9)

Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Let $(x_1,y_1)=(5,-1)$ and $(x_2,y_2)=(-3,7)$.
$d=\sqrt{(-3 - 5)^2+(7+1)^2}=\sqrt{(-8)^2+8^2}=\sqrt{64 + 64}=\sqrt{128}=8\sqrt{2}\approx11.31$

10a)

Use mid - point formula $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
Let $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(10,11)$.
$x=\frac{2+10}{2}=6$
$y=\frac{3 + 11}{2}=7$
Mid - point $M=(6,7)$. In the context of the drone's flight, it represents the halfway point between the warehouse A and the customer's location B.

10b)

Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Let $(x_1,y_1)=(2,3)$ and $(x_2,y_2)=(10,11)$.
$d=\sqrt{(10 - 2)^2+(11 - 3)^2}=\sqrt{8^2+8^2}=\sqrt{64+64}=\sqrt{128}=8\sqrt{2}\approx11.31$. In the real world, this distance represents the length of the path the drone needs to fly from warehouse A to the customer's location B.

Answer:

6a) Line BD
6b) Line BD
6c) Points B, C, D
6d) Points A, B, C, N
6e) Rays CB and CD

1. $(-1,6.5)$
2. $(-4,13)$
3. $8\sqrt{2}\approx11.31$

10a) Mid - point $M=(6,7)$. It represents the halfway point between the warehouse A and the customer's location B.
10b) $d = 8\sqrt{2}\approx11.31$. It represents the length of the path the drone needs to fly from warehouse A to the customer's location B.