Question

for the points (-4, 7) and (-6, 5), (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. (-4, 7) and (-6, 5) (x1, y1) and (x2, y2) apply the distance formula. d = \sqrt{(x2 - x1)^2+(y2 - y1)^2} d = \sqrt{(\square-(\square))^2+(\square-(\square))^2}

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(-4,7)$ and $(x_2,y_2)=(-6,5)$.

Step2: Substitute into distance formula

$d=\sqrt{(-6 - (-4))^{2}+(5 - 7)^{2}}=\sqrt{(-6 + 4)^{2}+(-2)^{2}}=\sqrt{(-2)^{2}+(-2)^{2}}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}$.

Step3: Find the mid - point formula

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

Step4: Substitute coordinates into mid - point formula

$M=(\frac{-4+( - 6)}{2},\frac{7 + 5}{2})=(\frac{-4-6}{2},\frac{12}{2})=(-5,6)$.

Answer:

(a) $2\sqrt{2}$
(b) $(-5,6)$