Question

Point Q is plotted on the coordinate grid. Point P is at (40, −20). Point R is vertically above point Q. It is at the same distance from point Q as point P is from point Q. Which of these shows the coordinates of point R and its distance from point Q?

Answer 1

Answer:

$\displaystyle d_{RP}=50\sqrt{2}\ units$

Step-by-step explanation:

Distance between points in $R^2$

If P(p1,p2) and Q(q1,q2) are points on the plane $R^2$, the distance between them is

$\displaystyle d=\sqrt{(q_1-p_1)^2+(q_2-p_2)^2}$

We have Q(-10,-20) plotted on the coordinate grid. We also know that P is at (40, -20). We can see they have the same y-coordinate, so the distance between them is computed simply by subtracting their x-coordinates

$\displaystyle d_{PQ}=40-(-10)=50$

We must locate R knowing it's vertically above Q (x-coordinate = -10) and at the same distance from point Q as point P is from point Q. That means that from R to Q there are 50 units. They-coordinate of R will be -20+50=30.  

The point R is located at (-10,30)

The distance from R to P is

$\displaystyle d_{RP}=\sqrt{(-10-40)^2+(30+20)^2}$

$\displaystyle d_{RP}=\sqrt{(-50)^2+50^2}$

$\displaystyle d_{RP}=\sqrt{2500+2500}$

$\displaystyle d_{RP}=\sqrt{5000}$

$\displaystyle d_{RP}=50\sqrt{2}\ units$