Question
Use the image to answer the question.
An illustration shows two plotted points: one in quadrant 2 and one in quadrant 4. A coordinate plane shows the x axis ranging from negative 2 to 6 and the y axis ranging from 6 to negative 4. A point upper Q is plotted at left parenthesis 4 comma negative 2 right parenthesis and a point upper S is plotted at left parenthesis negative 1 comma 3 right parenthesis.
Rectangle PQRS has vertices Q(4,−2) and S(−1,3) . What are the coordinates of vertices P and R ? Note, the vertex labels are located counterclockwise on the graph.
(1 point)
P(
); R(
)
Skip to navigation
To find the coordinates of vertices P and R, we need to remember that a rectangle has opposite sides that are equal in length and parallel to each other.
Given that Q is at (4, -2) and S is at (-1, 3), we can see that the width of the rectangle is 5 units and the height is 5 units.
Since the sides of the rectangle are parallel to the x and y axes, we can determine that vertex P is 5 units to the left of Q and 5 units down from Q. Therefore, the coordinates of P are (4 - 5, -2 - 5), which simplifies to (-1, -7).
Similarly, vertex R is 5 units to the right of S and 5 units up from S. Therefore, the coordinates of R are (-1 + 5, 3 + 5), which simplifies to (4, 8).
Therefore, the coordinates of vertices P and R are P(-1, -7) and R(4, 8).