Question

for the points (-8, 7) and (-2, 9), (a) find the exact distance between the points. (b) find the midpoint of the line segment whose endpoints are the given points. part: 0 / 5 part 1 of 5 (a) find the exact distance between the points. label the points. note that the choice for (x1, y1) and (x2, y2) will not affect the outcome. (-8, 7) and (-2, 9) (x1, y1) and (x2, y2) apply the distance formula. d = √((x2 - x1)²+(y2 - y1)²) d = √(( - )²+( - )²)

Explanation:

Step1: Identify coordinates

Let $(x_1,y_1)=(-8,7)$ and $(x_2,y_2)=(-2,9)$.

Step2: Apply distance formula

$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(-2-(-8))^2+(9 - 7)^2}=\sqrt{(6)^2+(2)^2}=\sqrt{36 + 4}=\sqrt{40}=2\sqrt{10}$

Step3: Find mid - point formula

The mid - point formula is $M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

Step4: Substitute values into mid - point formula

$M=(\frac{-8+( - 2)}{2},\frac{7 + 9}{2})=(\frac{-8-2}{2},\frac{16}{2})=(-5,8)$

Answer:

(a) $2\sqrt{10}$
(b) $(-5,8)$