Question

Two vertices of a triangle $ABC$ are $A(5,-1),B(-2,3).$ If the ortho center of the triangle is $(0,0),$ find the co-ordinates of the third vertex.

• A. $\left(4.7\right)$
• B. $(-4.7)$
• C. $(-4.-7)$
• D. $(4.-7)$

Answer 1

The correct option is C $(-4.-7)$

$($slope of $AB\left)\right($ slope of $Cx)=-1$

$\frac{(-1-3)}{(5+2)}\times \frac{y}{x}=-1$

$\frac{y}{x}=\frac{7}{4}$ _____ (1)

$($ slope of $BC)\times ($ slope of $A+B)=-1$

$\frac{(y-3)}{(x+2)}\times \frac{-1}{5}=-1$

$y-3=10+5x$

$y=13+5x$

$\frac{7x}{4}=13+5x$

$\frac{7x-20x}{4}=13$

$-13x=13\times 4$

$x=-4$

$\Rightarrow y=\frac{7}{4}\times -4=-7$

$\therefore C=(-4,-7)$