Question

point m is located at (4, 6) on a coordinate grid. point m is translated 8 units to the left and 9 units down to create point m. which measurement is closest to the distance between point m and point m in units? a 12 units b 9 units c 4 units d 17 units

Explanation:

Step1: Find coordinates of M'

The original point M is (4, 6). Translating 8 units left means subtracting 8 from the x - coordinate, and 9 units down means subtracting 9 from the y - coordinate. So the coordinates of M' are (4 - 8, 6 - 9)=( - 4, - 3).

Step2: Use distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(4,6)$ and $(x_2,y_2)=( - 4, - 3)$. Then $d=\sqrt{(-4 - 4)^2+(-3 - 6)^2}=\sqrt{(-8)^2+(-9)^2}=\sqrt{64 + 81}=\sqrt{145}\approx12.04$.

Answer:

A. 12 units