Question

1. graph the image of the quadrilateral below using a scale factor of ( k = 3 / 2 ).

Explanation:

Step1: Find the coordinates of original points

Assume the coordinates of \(Q(-1,6)\), \(R(1,4)\), \(S(2,-1)\), \(T(0,-1)\) (by observing the grid).

Step2: Apply the scale - factor formula

The formula for dilation (scaling) of a point \((x,y)\) with scale factor \(k\) is \((x',y')=(k\times x,k\times y)\).
For point \(Q(-1,6)\):
\(x'=\frac{3}{2}\times(-1)=-\frac{3}{2}\), \(y'=\frac{3}{2}\times6 = 9\), so \(Q'(-\frac{3}{2},9)\)
For point \(R(1,4)\):
\(x'=\frac{3}{2}\times1=\frac{3}{2}\), \(y'=\frac{3}{2}\times4=6\), so \(R'(\frac{3}{2},6)\)
For point \(S(2,-1)\):
\(x'=\frac{3}{2}\times2 = 3\), \(y'=\frac{3}{2}\times(-1)=-\frac{3}{2}\), so \(S'(3,-\frac{3}{2})\)
For point \(T(0,-1)\):
\(x'=\frac{3}{2}\times0 = 0\), \(y'=\frac{3}{2}\times(-1)=-\frac{3}{2}\), so \(T'(0,-\frac{3}{2})\)

Answer:

\(Q'(-\frac{3}{2},9)\), \(R'(\frac{3}{2},6)\), \(S'(3,-\frac{3}{2})\), \(T'(0,-\frac{3}{2})\)