Question

You want to create a quadrilateral PQRS that is similar to quadrilateral JKLM. What are the coordinates of S?

a) (3,2)
b) (-1,2)
c) (3,-2)
d) (-1,-2)

Answer 1

To find the coordinates of point S in quadrilateral PQRS, we can use the ratios of side lengths from quadrilateral JKLM to quadrilateral PQRS.

Step-by-step explanation:

To create a similar quadrilateral PQRS to quadrilateral JKLM, the corresponding angles of the two quadrilaterals must be equal and the corresponding sides must be proportional. Let's assume that point P corresponds to point J, point Q corresponds to point K, and point R corresponds to point L. We can find the coordinates of point S by using the same ratio of side lengths from quadrilateral JKLM to quadrilateral PQRS.

If the x-coordinate of point S in JKLM is x1, and the x-coordinate of point S in PQRS is x2, and if the y-coordinate of point S in JKLM is y1, and the y-coordinate of point S in PQRS is y2, then we have:

x1/x2 = JK/JQ = KL/KR = LM/LP

y1/y2 = JK/JQ = KL/KR = LM/LP

By substituting the known coordinates of points J, K, L, and M, and solving the system of equations, we can find the coordinates of point S.