Question

1. the table below shows the coordinates of a figure that was transformed.

pre-image	image
b(6, 1)	b(-4, -3)
c(4, 5)	c(-6, 1)

which is a correct description of the transformation?

a. rotation 180° clockwise
b. reflection over the x - axis
c. translation 5 units left and 2 units down
d. translation 10 units left and 4 units down

Explanation:

Step1: Analyze Option A (180° Rotation)

A 180° clockwise (or counterclockwise) rotation about the origin has the rule \((x,y)\to(-x,-y)\). For point \(A(5,2)\), applying this rule gives \((-5,-2)\), which matches \(A'(-5,-2)\). Let's check \(B(6,1)\): \(-6,-1\)? Wait, no, \(B'(-4,-3)\). Wait, maybe I miscalculated. Wait, no, let's re - check. Wait, the rule for 180° rotation is \((x,y)\to(-x,-y)\). For \(A(5,2)\), \(-5,-2\) (matches \(A'\)). For \(B(6,1)\), \(-6,-1\) but \(B'(-4,-3)\). Wait, that doesn't match. Wait, maybe I made a mistake. Wait, let's check the translation for option D. For \(A(5,2)\), moving 10 units left: \(5 - 10=-5\), 4 units down: \(2-4 = - 2\), which matches \(A'(-5,-2)\). For \(B(6,1)\): \(6-10=-4\), \(1 - 4=-3\), which matches \(B'(-4,-3)\). For \(C(4,5)\): \(4-10=-6\), \(5 - 4 = 1\), which matches \(C'(-6,1)\). Now let's re - examine option A. The 180° rotation rule is \((x,y)\to(-x,-y)\). For \(B(6,1)\), it should be \((-6,-1)\) but \(B'(-4,-3)\), so A is wrong. Option B: Reflection over x - axis is \((x,y)\to(x,-y)\). For \(A(5,2)\), it would be \((5,-2)\), not \((-5,-2)\), so B is wrong. Option C: Translation 5 left and 2 down. For \(A(5,2)\): \(5 - 5 = 0\), \(2-2 = 0\), not \((-5,-2)\), so C is wrong. Option D: Translation 10 left (\(x-10\)) and 4 down (\(y - 4\)). For \(A(5,2)\): \(5-10=-5\), \(2 - 4=-2\) (matches \(A'\)). For \(B(6,1)\): \(6-10=-4\), \(1-4=-3\) (matches \(B'\)). For \(C(4,5)\): \(4-10=-6\), \(5 - 4 = 1\) (matches \(C'\)).

Answer:

D. Translation 10 units left and 4 units down