Question

WILL GIVE BRAINLIEST!!!!Use the Pythagorean Theorem to find the distance between (-3, 4) and (6, 1). Show all calculations.

Answer 1

Answer:

AB = $\sqrt{90}$ = $3\sqrt{10}$

Step-by-step explanation:

A (-3,4); B (6,1)

Let H lays on x-axis and AH ⊥ Ox --> H (xA,0) = (-3,0)

Let K lays on AH and BK ⊥ AH --> K (xA, yB) = (-3, 1)

AK = |yA - yK| = |4 - 1| = 3

BK = |xB - xK| = |6 - -3| = 9

ABK is a right triangle (AKB = 90)

--> AB^2 = AK^2 + BK^2 = 3^2 + 9^2 = 90

--> AB = $\sqrt{90}$ = $3\sqrt{10}$

Or, you can use the formula:

AB = $\sqrt{(xA - xB)^2 + (yA - yB)^2}$ and get the same result.

This formula can be used to find the distance between any 2 points.