Question

8. The distance between (3,5) and (9, -3) is: A. 100 B. 2137 C. 2135 D. 10

Answer 1

Answer:

10 (Answer D)

Step-by-step explanation:

Here we see that the x-coordinate changes by 6, from 3 to 9, and that the y coordinate changes by 8, from 5 to -3.

We use the Pythagorean Theorem to calculate the distance between these two points.  One leg of a triangle here has length 6 and the other leg has length 8.  Applying this Theorem, we get:

6^2 + 8^2 = [ distance between (3, 5) and (9, -3) ]^2  =  d^2, and so:

d^2 = 36 + 64 = 100.

This distance must be positive.  Thus we take the positive square root of 100, which is 10.  10 is the distance between these two points.