Question

Write an ordered pair for the point in

Quadrant IV that is 4 units away from
point S(-1.5, -2.5) on the coordinate
plane.

Answer 1

Explanation:

"4 units away from point S(-1.5, -2.5)" sounds like a circle with center (-1.5, -2.5) and radius 4:

(x + 1.5)^2 + (y +2.5)^2 = 4^2, or 16

If the desired point is in Q IV, we choose an x - value greater than 0 and calculate the corresponding y-value. If we choose x = 1 then

(1 + 1.5)^2 + (y +2.5)^2 = 16

which becomes

2.5^2 + (y +2.5)^2 = 16

And so:

6.25 + (y +2.5)^2 = 16, OR

(y +2.5)^2 = 9.75, OR

y + 2.5 = √9.75 = 3.122

Solving for y, we get 0.6224

and so the desired point is (1, 0.6224). (Unfortunately, this is not in QIV, but rather in QI.)