Question

1. triangle abc has vertices a(-2,2), b(-1,-3), and c(4,0). find the coordinates of the vertices of △abc, the image of △abc after the transformation rx - axis. the use of the grid below is optional.

Explanation:

Step1: Recall the rule for reflection over the x - axis

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

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

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

Step3: Apply the rule to point \(B(-1,-3)\)

For point \(B(-1,-3)\), substitute \(x=-1\) and \(y=-3\) into the rule \((x,y)\to(x, - y)\). Then \(-y=-(-3) = 3\), so \(B'(-1,3)\).

Step4: Apply the rule to point \(C(4,0)\)

For point \(C(4,0)\), substitute \(x = 4\) and \(y = 0\) into the rule \((x,y)\to(x, - y)\). Then \(-y=-0=0\), so \(C'(4,0)\).

Answer:

The coordinates of the vertices of \(\triangle A'B'C'\) are \(A'(-2,-2)\), \(B'(-1,3)\) and \(C'(4,0)\)