Question

If A(4,3);B(-1,Y) and C(3,4) are the vertices of a right angled triangle ABC angle A = 90 degree. Then find the value of Y.

Answer 1

Answer:

The answer is Y = 1/3

Step-by-step explanation:

Explanation given in the picture.

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Answer 2

The value of y=-2

Step-by-step explanation:

In triangle ABC

Angle A=90 degree

A(4,3),B(-1,y) and C(3,4)

Distance formula:$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the formula

$AB=\sqrt{(-1-4)^2+(y-3)^2}$

$AB^2=(-5)^2+y^2+9-6y=25+y^2+9-6y=y^2-6y+34$

Using identity:$(a-b)^2=a^2+b^2+2ab$

$BC^2=(3+1)^2+(4-y)^2=16+16+y^2-8y=32+y^2-8y$

$AC^2=(3-4)^2+(4-3)^2=1+1=2$

Pythagoras theorem:$(Hypotenuse)^2=(base)^2+(Perpendicular\;side)^2$

Using the formula

$BC^2=AB^2+AC^2$

Substitute the values

$y^2-8y+32=y^2-6y+34+2$

$y^2-8y-y^2+6y=36-32$

$-2y=4$

$y=-\frac{4}{2}=-2$

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