Question

triangle pqr has vertices p(3,8), q(-5,7), and r(0,2). what are the coordinates of the vertices of the image after a reflection in the y - axis? a) p(3,-8) b) p(-3,8) c) q(5,7) d) q(5,-7) e) r(-2,0) f) r(0,2)

Explanation:

Step1: Recall reflection over y - axis rule

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

Step2: Find \(P'\)

Given \(P(3,8)\), applying the reflection rule over \(y\) - axis: \(x = 3\), so \(-x=-3\), \(y = 8\). So \(P'(-3,8)\).

Step3: Find \(Q'\)

Given \(Q(-5,7)\), applying the reflection rule over \(y\) - axis: \(x=-5\), so \(-x = 5\), \(y = 7\). So \(Q'(5,7)\).

Step4: Find \(R'\)

Given \(R(0,2)\), applying the reflection rule over \(y\) - axis: \(x = 0\), so \(-x=0\), \(y = 2\). So \(R'(0,2)\).

Now we check the options:

• Option A: \(P'(3,-8)\) is wrong (since \(y\) - coordinate should remain \(8\)).
• Option B: \(P'(-3,8)\) is correct.
• Option C: \(Q'(5,7)\) is correct.
• Option D: \(Q'(5,-7)\) is wrong (since \(y\) - coordinate should remain \(7\)).
• Option E: \(R'(-2,0)\) is wrong (original \(R\) is \((0,2)\)).
• Option F: \(R'(0,2)\) is correct.

Answer:

B. \(P'(-3,8)\), C. \(Q'(5,7)\), F. \(R'(0,2)\)