Question

graph and label all pre - images planes below. rectangle qrst with vertices q(-6, -1), r(-2, 1), s(1, -5), and t(-2, -7). (x,y)→(x + 5,y + 7) triangle abc with vertices a(-4, b(4, 7), and c(5, 1): x - axis

Explanation:

Step1: Identify pre - image vertices

The pre - image vertices of rectangle QRST are Q(-6,-1), R(-2,1), S(1,-5), T(-2,-7).

Step2: Apply translation rule

For point Q:
$(x,y)=(-6,-1)$, applying the rule $(x,y)\to(x + 5,y + 7)$ gives $(-6+5,-1 + 7)=(-1,6)$.
For point R:
$(x,y)=(-2,1)$, applying the rule gives $(-2+5,1 + 7)=(3,8)$.
For point S:
$(x,y)=(1,-5)$, applying the rule gives $(1+5,-5 + 7)=(6,2)$.
For point T:
$(x,y)=(-2,-7)$, applying the rule gives $(-2+5,-7 + 7)=(3,0)$.

Step3: Graph the pre - image

On the coordinate grid, plot the points Q(-6,-1), R(-2,1), S(1,-5), T(-2,-7) and label them.

Answer:

The pre - image of rectangle QRST has vertices Q(-6,-1), R(-2,1), S(1,-5), T(-2,-7) which are graphed and labeled on the coordinate grid.