The x - and y -coordinates of a point in quadrant III are consecutive even integers whose product is 360. Find the coordinates of the point.
A)(20, 18)
B)(-20, -18)
C)(-24, -22)
D)(24, 22)

Question

Quizplus · Accepted Answer

Let the consecutive even integers be x and x-2. We know that their product equals 360, so we can write the equation: 
x(x-2)=360

Expanding the equation:
x^2 - 2x = 360

Moving all terms to one side:
x^2 - 2x - 360 = 0

Now we can factor the equation:
(x-20)(x+18) = 0

The solutions are x=20 and x=-18. We reject x=20 because the point must be in quadrant III, so the coordinates are (-18,-20). However, we need the even integers to be consecutive, so we switch the order to get (-20,-18) as our final answer.

The X - and Y -Coordinates of a Point in Quadrant