Question

Center of Dilation1. Dilate Figure PQRS by a scale factor of using the point (4, 6)as the center of dilation. Determine the coordinates of FigureP'Q'R'S' and draw the approximate dilation on the coordinateplane.8th grade pre algebra

Answer 1

The coordinates of P',Q',R',S' are;

`\begin{gathered} P^(\prime)=(-6.5,6) \\ Q^(\prime)=(1,6) \\ R^(\prime)=(4,-7.5) \\ S^(\prime)=(-9.5,-7.5) \end{gathered}`

Step-by-step explanation:

Given the quadrilateral PQRS as shown on the diagram.

To determine the coordinates of the figure P'Q'R'S' which is the dilated image of PQRS. Let us apply the formula below;

`D_(o,k)(x,y)=(k(x-a)+a,k(y-b)+b)`

Where;

the center of dilation is (a,b)

the scale factor is k

Given;

`\begin{gathered} (a,b)=(4,6) \\ k=(3)/(2) \end{gathered}`

And from the image PQRS;

`\begin{gathered} P=(-3,6) \\ Q=(2,6) \\ R=(4,-3) \\ S=(-5,-3) \end{gathered}`

We can then calculate the coordinates of their respective P',Q',R' and S' using the formula;

`\begin{gathered} P^{}=(-3,6) \\ P^(\prime)=((3)/(2)(-3-4)+4,(3)/(2)(6-6)+6) \\ P^(\prime)=((-21)/(2)+4,0+6) \\ P^(\prime)=(-6.5,6) \end{gathered}`
`\begin{gathered} Q=(2,6) \\ Q^(\prime)=((3)/(2)(2-4)+4,(3)/(2)(6-6)+6) \\ Q^(\prime)=((-6)/(2)+4,0+6) \\ Q^(\prime)=(1,6) \end{gathered}`
`\begin{gathered} R=(4,-3) \\ R^(\prime)=((3)/(2)(4-4)+4,(3)/(2)(-3-6)+6) \\ R^(\prime)=(0+4,(-27)/(2)+6) \\ R^(\prime)=(4,-7.5) \end{gathered}`
`\begin{gathered} S=(-5,-3) \\ S^(\prime)=((3)/(2)(-5-4)+4,(3)/(2)(-3-6)+6) \\ S^(\prime)=((-27)/(2)+4,(-27)/(2)+6) \\ S^(\prime)=(-9.5,-7.5) \end{gathered}`

Therefore, the coordinates of P',Q',R',S' are;

`\begin{gathered} P^(\prime)=(-6.5,6) \\ Q^(\prime)=(1,6) \\ R^(\prime)=(4,-7.5) \\ S^(\prime)=(-9.5,-7.5) \end{gathered}`