195k views
4 votes
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

Center of Dilation1. Dilate Figure PQRS by a scale factor of using the point (4, 6)as-example-1
User LuBre
by
8.4k points

1 Answer

4 votes

Answer:

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}

User Shera
by
8.0k points

Related questions

asked Dec 11, 2023 95.1k views
Rizowski asked Dec 11, 2023
by Rizowski
7.6k points
1 answer
4 votes
95.1k views
asked Sep 13, 2021 50.9k views
Shirish Patel asked Sep 13, 2021
by Shirish Patel
7.7k points
1 answer
5 votes
50.9k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories