TS EAMCET · Maths · Straight Lines

In an isosceles right angled triangle, if the equation of the hypotenuse and its opposite vertex are $3 x + 4 y = 4$ and $(2, 2),$ then the slopes of the remaining two sides are

A $\frac{1}{7}, - 7$
B $\frac{- 1}{7}, 7$
C $\frac{1}{7}, 7$
D $\frac{- 1}{7}, - 7$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{1}{7}, - 7$

Step-by-step Solution

Detailed explanation

Given that in an isosceles triangle equation of hypotenuse is 3x+4y=4 i.e. y=-34x+44 ∴Slope the hypotenuse is -34. Let the slope of required line is m. As, tanθ=m1-m21+m1m2 ∵Angle made by the hypotenuse with other two sides is 45°.…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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In an isosceles right angled triangle, if the equation of the hypotenuse and its opposite vertex are 3x+4y=4 and 2, 2, then the slopes of the remaining two sides are

Step-by-step Solution

In an isosceles right angled triangle, if the equation of the hypotenuse and its opposite vertex are $3 x + 4 y = 4$ and $(2, 2),$ then the slopes of the remaining two sides are