Question

1. test prep what are the coordinates of the image after translating the triangle 1 unit right, 5 units down and then reflecting the triangle in the y - axis? a. s(-3, -1), r(-3, -4), t(-1, -4) b. s(-3, 1), r(-3, 4), t(-1, 4) c. s(3, -1), r(3, -4), t(1, -4) d. s(3, 1), r(3, 4), t(1, 4)

Explanation:

Step1: Identify original coordinates

From the graph, assume the original coordinates of the vertices of the triangle are \(T(0, - 2)\), \(R(-1,4)\), \(S(3,4)\).

Step2: Apply translation

The translation is 1 unit right and 5 units down. The rule for translation \((x,y)\to(x + 1,y-5)\).
For point \(T(0,-2)\): \(T'(0 + 1,-2-5)=T'(1,-7)\)
For point \(R(-1,4)\): \(R'(-1 + 1,4 - 5)=R'(0,-1)\)
For point \(S(3,4)\): \(S'(3 + 1,4-5)=S'(4,-1)\)

Step3: Apply reflection across y - axis

The rule for reflection across the y - axis is \((x,y)\to(-x,y)\)
For point \(T'(1,-7)\): \(T''(-1,-7)\)
For point \(R'(0,-1)\): \(R''(0,-1)\)
For point \(S'(4,-1)\): \(S''(-4,-1)\)

Answer:

\(T(-1,-7)\), \(R(0,-1)\), \(S(-4,-1)\)