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

Asked by Abhisek | 1 year ago |  139

##### Solution :-

Consider ABC as the right angles triangle where ∠C = 90°

Here infinity such lines are present.

m is the slope of AC

So the slope of BC =$$- \dfrac{1}{m}$$

Equation of AC –

y – 3 = m (x – 1)

By cross multiplication

x – 1 = $$\dfrac{1}{m}$$ (y – 3)

Equation of BC –

y – 1 = $$- \dfrac{1}{m}$$ (x + 4)

By cross multiplication

x + 4 = – m (y – 1)

By considering values of m we get

If m = 0,

So we get

y – 3 = 0, x + 4 = 0

If m = ∞,

So we get

x – 1 = 0, y – 1 = 0 we get x = 1, y = 1

Answered by Pragya Singh | 1 year ago

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