Kaycee draws PQRS on a coordinate grid. The coordinates of three of the vertices are P(-5, 4), Q(1,4), and R(3,-2). If PQRS is a parallelogram, what are the coordinates of point S?
O A. (-3, -1)
O B. (-3,-2)
O c. (-5,-2)
D. (-5,-1)
ANSWERD IS WORNG
To find the coordinates of point S, we need to make use of the fact that PQRS is a parallelogram.
Given that P(-5, 4), Q(1, 4), and R(3, -2) are three of the vertices of the parallelogram, we can use the property of a parallelogram that opposite sides are parallel and have the same length.
Since PQRS is a parallelogram, we can find the length of side PQ by using the distance formula.
The distance formula is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
For PQ, using the coordinates P(-5, 4) and Q(1, 4), the distance will be:
d = √[(1 - (-5))^2 + (4 - 4)^2]
= √[(1 + 5)^2 + (0)^2]
= √[6^2 + 0]
= √[36]
= 6
Since opposite sides of a parallelogram have the same length, side SR will also have a length of 6.
Now, to find the coordinates of S, we need to move 6 units in the same direction from point R(3, -2).
Since we need to move 6 units in the negative y-direction, the y-coordinate of S will be -2 - 6 = -8.
Therefore, the coordinates of point S are (3, -8).
Thus, the correct answer is not provided in the choices given.
To find the coordinates of point S, we need to use the fact that PQRS is a parallelogram.
Since opposite sides of a parallelogram are parallel, we can determine the coordinates of point S by finding the position of point S relative to the other vertices.
We know that PQ and RS are parallel, so the x-coordinate of S must be the same as the x-coordinate of Q. Similarly, PR and QS are parallel, so the y-coordinate of S must be the same as the y-coordinate of R.
Given that Q(1,4) and R(3,-2), we can conclude that the x-coordinate of S is 1, and the y-coordinate of S is -2.
Therefore, the coordinates of point S are (1, -2).
So the correct option is not in the given options.