Question

triangle abc has coordinates a(2,0), b(-1,5), and c(4,3). determine the coordinates of the vertices of the image after a reflection in the y - axis.
a) a(-2,0), b(1,5), and c(-4,3)
b) a(2,0), b(-1,-5), and c(4,-3)
c) a(2,2), b(-1,7), and c(4,5)
d) a(-2,0), b(1,-5), and c(-4,-3)

Explanation:

Step1: Recall the reflection 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 \(A(2,0)\)

For \(A(2,0)\), using the rule \((x,y)\to(-x,y)\), we get \(A'(- 2,0)\) since \(x = 2\) and \(y=0\), and \(-x=-2\).

Step3: Apply the rule to point \(B(-1,5)\)

For \(B(-1,5)\), \(x=-1\) and \(y = 5\). Using the rule \((x,y)\to(-x,y)\), \(-x=-(-1)=1\), so \(B'(1,5)\).

Step4: Apply the rule to point \(C(4,3)\)

For \(C(4,3)\), \(x = 4\) and \(y=3\). Using the rule \((x,y)\to(-x,y)\), \(-x=-4\), so \(C'(-4,3)\).

Answer:

A. \(A'(-2,0)\), \(B'(1,5)\), and \(C'(-4,3)\)