Question

a triangle has the coordinates a(4, - 1), b(3, - 3), and c(0, 2). reflect the triangle over the y - axis and find the coordinates of its image. a(4, - 1)→a (, ) b(3, - 3)→b (, ) c(0, 2)→c (, )

Explanation:

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

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

Step2: Apply the rule to point \(A(4,-1)\)

For point \(A(4,-1)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x = 4\) and \(y=-1\). So \(A(4,-1)\to A'(-4,-1)\).

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

For point \(B(3,-3)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x = 3\) and \(y=-3\). So \(B(3,-3)\to B'(-3,-3)\).

Step4: Apply the rule to point \(C(0,2)\)

For point \(C(0,2)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x = 0\) and \(y = 2\). So \(C(0,2)\to C'(0,2)\) (since \(-0=0\)).

Answer:

\(A(-4,-1)\), \(B(-3,-3)\), \(C(0,2)\)