question: on a coordinate plane, plot the points (a(-3,1)), (b(2,1)), (c(2, - 2)), and (d(x,y)) such that…

question: on a coordinate plane, plot the points (a(-3,1)), (b(2,1)), (c(2, - 2)), and (d(x,y)) such that quadrilateral (abcd) is a square. find the coordinates of point (d) and justify your answer by calculating the lengths of all sides and verifying right - angles using the graph.

question: on a coordinate plane, plot the points (a(-3,1)), (b(2,1)), (c(2, - 2)), and (d(x,y)) such that quadrilateral (abcd) is a square. find the coordinates of point (d) and justify your answer by calculating the lengths of all sides and verifying right - angles using the graph.

Answer

Explanation:

Step1: Find side - length and slope

Length of $AB=\sqrt{(2 + 3)^2+(1 - 1)^2}=5$, slope of $AB = 0$.

Step2: Determine coordinates of D

Since $ABCD$ is a square, $AD$ is perpendicular to $AB$. So, $x=-3$. Also, length of $AD = 3$. So, $y=-2$. So $D(-3,-2)$.

Step3: Verify

Length of $BC=\sqrt{(2 - 2)^2+( - 2 - 1)^2}=3$, length of $CD=\sqrt{( - 3 - 2)^2+( - 2+2)^2}=5$, length of $AD=\sqrt{( - 3 + 3)^2+( - 2 - 1)^2}=3$. Slopes of adjacent sides are perpendicular.

Answer:

$D(-3,-2)$