Question

two triangles are graphed in the xy - coordinate plane. which sequence of transformations will carry \\( \triangle qrs \\) onto \\( \triangle qrs \\)? a a translation left 3 units and down 6 units b a translation left 3 units and up 6 units c a translation right 3 units and down 6 units

Explanation:

Step1: Find the translation of a point

Take point \(Q(-2,3)\) and its image \(Q'(-5, - 3)\).
For the \(x\) - coordinate: \(-5-(-2)=-5 + 2=-3\) (left \(3\) units).
For the \(y\) - coordinate: \(-3 - 3=-6\) (down \(6\) units).

Step2: Verify with another point

Take point \(R(4,5)\) and its image \(R'(1,-1)\).
For the \(x\) - coordinate: \(1 - 4=-3\) (left \(3\) units).
For the \(y\) - coordinate: \(-1-5=-6\) (down \(6\) units).

Answer:

A. a translation left 3 units and down 6 units