Question

May I please get help with this. I have tried multiple but still could not get the correct or at least accurate answers

Answer 1

a) PS = QR = √37

b) Slope of PS = Slope of QR = -1/6

c) Option A is correct

Explanations:

The figure shown on the coordinate plane is a parallelogram. A parallelogram is a shape with its opposite side parallel and congruent.

From the given diagram, PS = QR and RS = PQ

a) To find the length of PS, we will find the distance between the coordinate points P(1, -3) and S(-5, -2). Using the distance formula;

`\begin{gathered} PS=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ PS=\sqrt[]{(1-(-5))^2+\mleft(-3-\mleft(-2\mright)\mright)} \\ PS=\sqrt[]{(1+5)^2+(-3+2)^2} \\ PS=\sqrt[]{6^2_{}+1^2} \\ PS=\sqrt[]{37} \end{gathered}`

Since PS = QR, hence QR = √37

b) Parallel lines also have the same slope. Therefore, the slope of PS is equal to the slope of QR. Using the slope equation;

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \text{Slope of PS=}(-2-(-3))/(-5-1) \\ \text{Slope of PS=}(-2+3)/(-6) \\ \text{Slope of PS=-}(1)/(6) \end{gathered}`

Since the slope of PS is equal to the slope of QR, hence the slope of QR is -1/6

c) As earlier discussed, the opposite sides of a parallelogram are parallel and congruent. Hence we can conclude from the options given that "the quadrilateral is a parallelogram because it has one pair of opposite sides that are both congruent and parallel.