Question

triangle qrs is rotated 270° clockwise about the origin, translated 2 units to the right and reflected over the x - axis. the image that results is △qrs. what are the coordinates of vertex r on the image? a. (4, - 6) b. (4, - 2) c. (0, - 2) d. (4, 4)

Explanation:

Step1: Determine the rotation rule

A 270 - degree clockwise rotation about the origin has the rule $(x,y)\to(y, - x)$. Assume the coordinates of point $R$ are $(2,2)$. After a 270 - degree clockwise rotation about the origin, $R(2,2)\to R_1(2, - 2)$.

Step2: Apply the translation

The translation 2 units to the right has the rule $(x,y)\to(x + 2,y)$. So, $R_1(2,-2)\to R_2(2 + 2,-2)=(4,-2)$.

Step3: Apply the reflection

The reflection over the $x$ - axis has the rule $(x,y)\to(x,-y)$. So, $R_2(4,-2)\to R'(4,2)$.

Answer:

B. $(4,2)$