Question

Quadrilateral PQRS is plotted in the coordinate plane. The quadrilateral is dilated by a scale factor of 3/4. What are the new ordered pairs for P'Q'R'S'?

Answer 1

Step-by-step explanation:

The first thing is to state the coordinates of Quadrilateral PQRS

P (5, 5), Q (3, 5), R (3, 1), S (5, 1)

Then we find the distance between two points using the distance formula

`dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}`
`\begin{gathered} P(5,5),Q(3,5)\text{ = (x1, y1) and (x2, y2)} \\ \text{distance PQ = }\sqrt[]{(5-5)^2+(3-5)^2}\text{ = }\sqrt[]{0+(-2)^2}\text{ =}\sqrt[]{4} \\ \text{distance PQ = }2 \end{gathered}`
`\begin{gathered} Q(3,5),R(3,1)\text{= (x1, y1) and (x2, y2)} \\ \text{distance QR = }\sqrt[]{(1-5)^2+(3-3)^2}\text{ = }\sqrt[]{(-4)^2+0}\text{ = }\sqrt[]{16} \\ \text{distance QR = 4} \end{gathered}`

It is a quadrilateral, meaning the two lengths are equal. Like wise the two widths are equal.

length PQ = length SR = 2

Length QR = length PS = 4

Scale factor = 3/4

Scale factor = corresponding side of new image/ corresponding side of original image

PQRS = original image, P'Q'R'S' = new image

3/4 = P'Q'/PQ

3/4 = P'Q'/2

P'Q' = 2(3/4) = 6/4 = 3/2

Since P'Q' = S'R'

S'R' = 3/2

3/4 = Q'R'/QR

3/4 = Q'R'/4

Q'R' = 3/4 (4) = 12/4 = 3

Since Q'R' = P'S

P (5, 5), Q (3, 5), R (3, 1), S (5, 1)

PQRS to P'Q'R'S' = 3/4(

P' = 3/4 (5, 5) = (15/4, 15/4)

Q' = 3/4 (3, 5) = (9/4, 15/4)

R' = 3/4 (3, 1) = (9/4, 3/4)

S' = 3/4 (5, 1)