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

Solution:

Let PQR be the right-angled triangle, where ∠R = 90°

Assume that P = (1, 3) and Q = (-4, 1). Then R will be (1, 1) which you can get from the following figure.

Now we will find the equations of the two legs PR and QR.

Equation of PR:

PR is a vertical line passing through (1, 1). Hence its equation is y = 1.

Equation of QR:

QR is a horizontal line passing through (1, 1). Hence its equation is x = 1.

Thus, the equations of legs of the triangle are x = 1 and y = 1

NCERT Solutions Class 11 Maths Chapter 10 Exercise ME Question 17

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

Summary:

If the hypotenuse of a right-angled triangle has its end at the points (1, 3) and (- 4, 1), then the equations of the legs (perpendicular sides) of the triangle are x = 1 and y = 1