Question

The vertices of a $\Delta ABC$ are $A(-5,-2),B(7,6)$ and $C(5,-4)$. Then

• A. measure of angle B is $\frac{\pi }{4}$
• B. equation of the altitude drawn from the vertex C has the equation $3x+2y-7=0$
• C. orthocentre of the triangle does not lie inside the $\Delta ABC$
• D. all of these

Answer 1

The correct option is D all of these

Given the vertices of $△$ABC

i.e, C(5,-4) A(-5-2) and B(7,6)

let CD be the altitude such that $△$CDB becomes a right angle triangle and angle B=45 degree

To find the midpoint D,

$(\frac{-5+7}{2},\frac{-2+6}{2})=(1,2)$

$\therefore$ The equation of altitude drawn fron vertex C,

$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}⟹\frac{y+4}{2+4}=\frac{x-5}{1-5}⟹y+\frac{4}{6}=\frac{x-5}{-4}⟹-4y-16=6x-30\therefore 3x+2y-7=0$

The orthocenter is not always inside the triangle of the triangle is obture,it will be outside