Question

which of the following steps were applied to \\( \triangle abc \\) obtain \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\)?

a. shifted 3 units left and 3 units down
b. shifted 4 units left and 2 units down
c. shifted 4 units left and 3 units down

Explanation:

Step1: Determine the horizontal shift

Take point \(A\) (original) and \(A'\) (transformed). Assume \(A=(4,5)\) and \(A'=(0,2)\). The \(x -\)coordinate change: \(4 - 0=4\) units to the left.

Step2: Determine the vertical shift

The \(y -\)coordinate change: \(5 - 2 = 3\) units down.
We can check other points (e.g., \(B\) and \(B'\), \(C\) and \(C'\)) for confirmation. If \(B=(4,9)\) and \(B'=(0,6)\), \(x\) - shift: \(4-0 = 4\) (left), \(y\) - shift: \(9 - 6=3\) (down). If \(C=(6,5)\) and \(C'=(2,2)\), \(x\) - shift: \(6 - 2=4\) (left), \(y\) - shift: \(5 - 2 = 3\) (down).

Answer:

C. Shifted 4 units left and 3 units down