Answer:
Part A) [tex]QR=2\sqrt{5}\ units[/tex]
Part B) [tex]PR=2\sqrt{13}\ units[/tex]
Step-by-step explanation:
The complete question in English is
Observe the isosceles PQRS trapeze in the Cartesian plane.
A) How long is the QR side?
B) What is the distance between points P and R?
The picture of the question in the attached figure
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Part A) How long is the QR side?
we have the coordinates
Q(7,6) and R(9,2)
substitute in the formula
[tex]d=\sqrt{(2-6)^{2}+(9-7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(2)^{2}}[/tex]
[tex]d_Q_R=\sqrt{20}\ units[/tex]
simplify
[tex]d_Q_R=2\sqrt{5}\ units[/tex]
Part B) What is the distance between points P and R?
we have the coordinates
P(3,6) and R(9,2)
substitute in the formula
[tex]d=\sqrt{(2-6)^{2}+(9-3)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(6)^{2}}[/tex]
[tex]d_P_R=\sqrt{52}\ units[/tex]
simplify
[tex]d_P_R=2\sqrt{13}\ units[/tex]
