Problem Solving

BTGModeratorVI wrote: ↑

Thu Dec 03, 2020 2:45 pm

In the xy-plane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?

A. (r,s)
B. (s,–r)
C. (–s,–r)
D. (–r,s)
E. (–r,–s)

Answer: E
Source: official guide

Let's sketch a line segment with midpoint at the origin and an endpoint at (r, s)




We can now travel the SAME DISTANCES (from the origin) to ensure that the origin is the midpoint.



From here, we can see that (-r, -s) are the coordinates of the other point.



Answer: E

Cheers,
Brent

BTGModeratorVI wrote: ↑

Thu Dec 03, 2020 2:45 pm

In the xy-plane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?

A. (r,s)
B. (s,–r)
C. (–s,–r)
D. (–r,s)
E. (–r,–s)

Answer: E
Source: official guide

Solution:

We use the midpoint formula: (x_1 + x_2)/2 = x-coordinate of the midpoint and (y_1 + y_2)/2 = y-coordinate of the midpoint.

We know that the coordinates of P are (r, s), and we can let the coordinates of Q be (x, y). Since the origin (0, 0) is the midpoint of PQ, we have:

(r + x)/2 = 0 and (s + y)/2 = 0

Multiplying each equation by 2, we have:

r + x = 0 and s + y = 0

x = -r and y = -s

Thus, the coordinates of Q are (-r, -s).

Answer: E