Question

The hypotenuse AB of the right triangle ABC is parallel to the axis of the abscess. Find the length of the hypotenuse if A (-1; 1) and C (3; -4)

Answer 1

10.25

Explanation:

The slope of AC is given by the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (-4 -1)/(3 -(-1)) = -5/4

Then the slope of CB is the opposite reciprocal, 4/5. The equation of line CB in point-slope form is ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

y -(-4) = 4/5(x -3) . . . . line CB

When y = 1 (to match the y-value of A), then ...

1 +4 = 4/5(x -3)

5(5/4) = (x -3) . . . . . multiply by 5/4

6.25 +3 = x = 9.25 . . . . add 3

Point B is (9.25, 1).

The length of the hypotenuse is ...

9.25 -(-1) = 10.25