Question

triangle abc has vertices a(-2,5), b(1,0), and c(6,-2). what are the coordinates of the vertices of △abc for y - axis?
a. a(5,-2), b(0,1), and c(-2,6)
b. a(2,-5), b(-1,0), and c(-6,2)
c. a(2,5), b(-1,0), and c(-6,-2)
d. a(-2,-5), b(1,0), and c(6,2)

Explanation:

Step1: <Reflection over y - axis rule>

When reflecting a point \((x,y)\) over the \(y -\)axis, the rule is \((x,y)\to(-x,y)\).

Step2: <Apply the rule to point \(A(-2,5)\)>

For point \(A(-2,5)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x=-2\) and \(y = 5\). Then \(x\) becomes \(-(-2)=2\), so \(A'=(2,5)\).

Step3: <Apply the rule to point \(B(1,0)\)>

For point \(B(1,0)\), substitute \(x = 1\) and \(y=0\) into the rule \((x,y)\to(-x,y)\). Then \(x\) becomes \(-1\), so \(B'=(-1,0)\).

Step4: <Apply the rule to point \(C(6,-2)\)>

For point \(C(6,-2)\), substitute \(x = 6\) and \(y=-2\) into the rule \((x,y)\to(-x,y)\). Then \(x\) becomes \(-6\), so \(C'=(-6,-2)\).

Answer:

C. \(A'(2,5), B'(-1,0)\), and \(C'(-6,-2)\)