Question

4) Triangle ABC is translated 2 units right and 5 units down to form triangle 1 pointA'B'C'. This triangle is then translated 5 units right and 4 units up to formtriangle A''B''C''. If vertex A is at (-4, 2), what are the coordinates of vertexA"?

Answer 1

In triangle ABC, the point A is located at (-4, 2)

Then, the triangle ABC is translated 2 units right and 5 units down.

(Quick summary of how to calculate translations:

- Translation x units to the right: sum x to the x-coordinate.

- Translation x units to the left: subtract x of the x-coordinate.

- Translation x units up: sum x to the y-coordinate.

- Translation x units down: subtract x of the y-coordinate.)

The translation to the right means we need to sum 2 units in the x-coordinate of every point of triangle ABC, and the translation down means we need to subtract 5 units in the y-coordinate.

So the point A' will be:

$A(-4,2)\to A^{\prime}(-4+2,2-5)\to A^{\prime}(-2,-3)$

Then, triangle A'B'C is translated 5 units right and 4 units up to form triangle A''B''C'', so in order to find A'', we need to sum 5 units to the x-coordinate of A' and sum 5 units to the y-coordinate of A'.

$A^{\prime}(-2,-3)\to A^{\doubleprime}(-2+5,-3+4)\to A^{\doubleprime}(3,1)$

So the coordinates of A'' are (3, 1), therefore the answer is the second option.