Question

graph square pqrs with p(-6, -2), q(-2, 0), r(0, -4), and s(-4, -6) and its image after a dilation of 3/2. what are the coordinates of p? a) (-3, -1) b) (4, 4/3) c) (-4, -4/3) d) (9, 3) e) (-9, -3)

Explanation:

Step1: Recall dilation formula

For a dilation with scale - factor \(k\) of a point \((x,y)\), the new point \((x',y')\) is given by \((x',y')=k(x,y)\).

Step2: Identify the point and scale - factor

The point \(P\) has coordinates \((-6,-2)\) and the scale - factor \(k = \frac{3}{2}\).

Step3: Calculate the new \(x\) - coordinate

\(x'=k\times x=\frac{3}{2}\times(-6)=-9\).

Step4: Calculate the new \(y\) - coordinate

\(y'=k\times y=\frac{3}{2}\times(-2)=-3\).
So the coordinates of \(P'\) are \((-9,-3)\).

Answer:

E. (-9, -3)