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Question

Assertion :If x+ky=1 and x=a are the equations of the hypotenuse and a side of a right angled isosceles triangle then k=±a. Reason: Each side of a right angled isosceles triangle makes an angle ±π4 with the hypotenuse.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is incorrect but Reason is correct
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D
Both Assertion and Reason are incorrect
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Solution

The correct option is C Assertion is incorrect but Reason is correct
Given sides

x+ky=1 ----(1)

and x=a ---(2)

On comparing both eq with y=mx+c, we get

m1=1k and m2=1

And the third side of the triangle is perpendicular to xk=0

So, slope of third line be m2m3=1


m3=1

The given triangle is isosceles triangle so the angle between line (1) and (2) is equal to the angle between line (1) and (3)

m1m21+m1m2=m1m31+m1m3

∣ ∣ ∣ ∣1k111k∣ ∣ ∣ ∣=∣ ∣ ∣ ∣1k+11+1k∣ ∣ ∣ ∣

1kk1=1+kk+1

(1+k)2=(k1)2

1k22k=k2+12k

2k2=|2|

k2=1

k=±1

Hence, the reason is correct.

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