Question

Which point is a distance of 15 units from the point (–6, –10)?

A. (–3, –2)
B. (3, 2)
C. (2, 3)
D. (–2, –3)

Answer 1

Getting good at Cartesian geometry generally means learning how to avoid the square roots which are a pain.

We seek the points that are 15 units from (-6,-10)

Those are the points that are a squared distance of 15×15=225.

The Pythagorean Theorem applied to the Cartesian grid gives up the squared distances:

A. (-6,-10) to (–3, –2)
`\qquad (-3- -6)^2 + (-2- -10)^2 = 3^2+8^2= 73 \qquad` nope

B. (-6,-10) to (3, 2)
`\qquad (3- -6)^2 + (2- -10)^2 = 9^2+12^2= 225\qquad` YES, CHOICE B IS CORRECT

C. (-6,-10) to (2, 3)
`\qquad (2- -6)^2 + (3- -10)^2 = 8^2+13^2= 233\qquad` nope

D. (-6,-10) to (–2, –3)
`\qquad (-2- -6)^2 + (-3- -10)^2 = 4^2+7^2= 65\qquad` nope

Choice B.