The closest distance between point A and point A' is 8.5 ⇒ B
Step-by-step explanation:
Let us revise the translation of a point
- If 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 ≅ 8.5
The 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
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