Question

The hypotenuse of a right-angled triangle has its end at the points (1, 3) and (-4, 1). Find an equation of the leg (perpendicular side) of the triangle.

(a) x−2y=1
(b) x+2y=5
(c) x−2y=−3
(d) x+2y=3

Answer 1

The equation of the leg (perpendicular side) of the triangle is x - 2y = -3. The correct answer is (c) x−2y=−3.

Step-by-step explanation:

To find the equation of the leg (perpendicular side) of the triangle, we need to first find the length of the hypotenuse of the triangle. Using the distance formula, we can calculate the length to be:

d = sqrt((1 - (-4))^2 + (3 - 1)^2) = sqrt(5^2 + 2^2) = sqrt(25 + 4) = sqrt(29)

Since the leg of the triangle is perpendicular to the hypotenuse, we can use the negative reciprocal of the slope of the hypotenuse to find the equation of the leg. The slope of the hypotenuse is (3 - 1) / (1 - (-4)) = 2/5. The negative reciprocal of 2/5 is -5/2.

Therefore, the equation of the leg of the triangle is x - 2y = -3.