Question

question 13 (multiple choice worth 4 points) (02.03r mc) which of the following would be a line of reflection that would map abcd onto itself? grid with points a(3,1), b(3,3), c(1,3), d(1,1) and options: y = 1; 2x + y = 2; x + y = 4; x + y = 1

Explanation:

Step1: Identify coordinates of vertices

$A(3,1), B(3,3), C(1,3), D(1,1)$

Step2: Test reflection over $x+y=4$

For a point $(x,y)$, reflection over $x+y=k$ is $(k-y, k-x)$. Here $k=4$, so reflection is $(4-y, 4-x)$:

• Reflect $A(3,1)$: $(4-1, 4-3)=(3,1)$ → maps to $B$
• Reflect $B(3,3)$: $(4-3, 4-3)=(1,1)$ → maps to $A$
• Reflect $C(1,3)$: $(4-3, 4-1)=(1,3)$ → maps to $D$
• Reflect $D(1,1)$: $(4-1, 4-1)=(3,3)$ → maps to $C$

Step3: Verify self-mapping

All vertices map to other vertices of ABCD, so the square maps onto itself.

Step4: Eliminate other options

• $y=1$: Reflects $B(3,3)$ to $(3,-1)$ (not in ABCD)
• $2x+y=2$: Reflects $A(3,1)$ to $(-\frac{3}{5}, -\frac{11}{5})$ (not in ABCD)
• $x+y=1$: Reflects $A(3,1)$ to $(0,-2)$ (not in ABCD)

Answer:

$x+y=4$