Question

The equation of the sides of a triangle, the coordinates of whose angular points are:
$(3,5)(1,2)$ and $(-7,4)$.

• A. $3x-2y+1=0$
• B. $x-10y+47=0$
• C. $x+4y-9=0$
• D. $Allofthese$

Answer 1

The correct option is D $Allofthese$

Let the given points be $A(3,5),B(1,2)$ and $C(-7,4)$

Let $m_1,m_2$ and $m_3$ be the slopes of sides $AB,BC,CA$ respectively.

$\therefore m_1=\frac{2-5}{1-3},m_2=\frac{4-2}{-7-1},m_3=\frac{4-5}{-7-3}$

$⟹m_1=\frac{3}{2},m_2=-\frac{1}{4},m_3=\frac{1}{8}$

So the equation of sides $AB,BC,CA$ are

$y-2=\frac{3}{2}(x-1),y-2=-\frac{1}{4}(x-1),$ and $y-4=\frac{1}{8}(x+7)$

$⟹3x-2y+1=0,x-10y+47=0$ and $x+4y-9=0$