Question

if triangle ( abc ) is rotated 90 degrees clockwise about the origin followed by dilation by a factor of 2 about the origin, what will be the resulting coordinates of the vertices of the transformed triangle ( abc )?
( \bigcirc ) ( a(0, -4) ); ( b(-6, 4) ); ( c(2, 2) )
( \bigcirc ) ( a(0, 2) ); ( b(3, -2) ); ( c(-1, -1) )
( \bigcirc ) ( a(0, 4) ); ( b(0, -4) ); ( c(-2, -2) )
( \bigcirc ) ( a(0, 4) ); ( b(-4, 0) ); ( c(-2, -2) )

Explanation:

Step1: Identify original coordinates

From the graph, $A(-2, 0)$, $B(0, 3)$, $C(1, -1)$

Step2: Rotate 90° clockwise about origin

Rule: $(x,y)\to(y,-x)$

• $A(-2,0)\to A_1(0, 2)$
• $B(0,3)\to B_1(3, 0)$
• $C(1,-1)\to C_1(-1, -1)$

Step3: Dilate by factor 2 about origin

Rule: $(x,y)\to(2x,2y)$

• $A_1(0,2)\to A'(0, 4)$
• $B_1(3,0)\to B'(6, 0)$
• $C_1(-1,-1)\to C'(-2, -2)$

Answer:

$A'(0, 4); B'(6, 0); C'(-2, -2)$ (matches the last option)