Question

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

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: Check rotation 180° clockwise rule

The rule for a 180° clockwise rotation about the origin is \((x,y)\to(-x, -y)\). For point \(A(5,2)\), after rotation it should be \((-5,-2)\); for \(B(6,1)\), it should be \((-6,-1)\) (but \(B'\) is \((-4,-3)\) which does not match).

Step2: Check reflection over x - axis rule

The rule for reflection over the \(x\) - axis is \((x,y)\to(x,-y)\). For \(A(5,2)\), it should be \((5,-2)\) (does not match \(A'(-5,-2)\)).

Step3: Check translation rule

The translation rule is \((x,y)\to(x + a,y + b)\). For \(A(5,2)\) to \(A'(-5,-2)\): \(x\) - coordinate: \(5+a=-5\Rightarrow a=-10\); \(y\) - coordinate: \(2 + b=-2\Rightarrow b=-4\). Check for \(B(6,1)\): \(6-10=-4\), \(1-4=-3\) (matches \(B'(-4,-3)\)); for \(C(4,5)\): \(4-10=-6\), \(5 - 4=1\) (matches \(C'(-6,1)\)).

Answer:

D. Translation 10 units left and 4 units down