Question

the table shows the coordinates of △qrs and its image.
qrs qrs
q(0,0) q(0,0)
r(1,3) r(3, - 1)
s(4,1) s(1, - 4)
which single transformation maps △qrs onto its image?
reflect across the x - axis.
translate 7 units down.
rotate 90° clockwise around the origin.

Explanation:

Step1: Recall transformation rules

For reflection across x - axis, $(x,y)\to(x, - y)$. For translation 7 units down, $(x,y)\to(x,y - 7)$. For 90 - degree clockwise rotation around origin, $(x,y)\to(y,-x)$.

Step2: Check each transformation for point R

For point $R(1,3)$:

• Reflection across x - axis: $(1,3)\to(1, - 3)$ (not correct).
• Translation 7 units down: $(1,3)\to(1,3 - 7)=(1,-4)$ (not correct).
• 90 - degree clockwise rotation around origin: $(1,3)\to(3,-1)$ (correct).

Step3: Check for point S

For point $S(4,1)$: 90 - degree clockwise rotation around origin gives $(4,1)\to(1,-4)$ (correct).

Answer:

Rotate 90° clockwise around the origin.