MATH SOLVE

6 months ago

Q:
# Point A is located at (-5, 2) on a coordinate grid. Point A is translated 8 units to the right and 3 units up to create point A.Which measurement is closest to the distance between point A and point A' in units?A.8.1B.8.5C8.9D9.4

Accepted Solution

A:

The closest distance between point A and point A' is 8.5 ⇒ B Step-by-step explanation:Let us revise the translation of a pointIf the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)If the point (x , y) translated vertically up by k units then its image is (x , y + k)If the point (x , y) translated vertically down by k units then its image is (x , y - k)
∵ Point A is located at (-5 , 2)∵ Point A is translated 8 units to the right and 3 units up- That means add x-coordinate by 8 and add y-coordinate by 3∴ Point A' located at (-5 + 8 , 2 + 3)∴ Point A' located at (3 , 5)The distance between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex]is [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]∵ Point a = (-5 , 2) and point A' = (3 , 5)∴ [tex]x_{1}[/tex] = -5 and [tex]x_{2}[/tex] = 3∴ [tex]y_{1}[/tex] = 2 and [tex]y_{2}[/tex] = 5- Substitute these values in the rule of the distance∵ [tex]d=\sqrt{(3--5)^{2}+(5-2)^{2}}[/tex]∴ [tex]d=\sqrt{(3+5)^{2}+(3)^{2}}[/tex]∴ [tex]d=\sqrt{(8)^{2}+(3)^{2}}[/tex]∴ [tex]d=\sqrt{64+9}=73[/tex]∴ d = 8.544 ≅ 8.5The closest distance between point A and point A' is 8.5 Learn more:You can learn more about the distance between two points in brainly.com/question/6564657#LearnwithBrainly