Two equal sides of an isosceles triangle are | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The equations of the two equal sides are:$7x-y+3=0 \quad \dots(i)$$x+y-3=0 \quad \dots(ii)$In an isosceles triangle,the third side is perpendicula

Vedclass · Accepted Answer

$-3$

Vedclass · Answer

(D) The equations of the two equal sides are:$7x-y+3=0 \quad \dots(i)$$x+y-3=0 \quad \dots(ii)$In an isosceles triangle,the third side is perpendicular to the angle bisector of the angle between the two equal sides. Alternatively,the third side makes equal angles with the two equal sides.Let the slope of the third side be $m$. The angle between the line with slope $m$ and the line $7x-y+3=0$ (slope $m_1=7$) is equal to the angle between the line with slope $m$ and the line $x+y-3=0$ (slope $m_2=-1$).Using the formula $	an 	heta = |\frac{m_1-m_2}{1+m_1m_2}|$:$|\frac{m-7}{1+7m}| = |\frac{m-(-1)}{1+m(-1)}|$$|\frac{m-7}{1+7m}| = |\frac{m+1}{1-m}|$$(m-7)(1-m) = \pm(m+1)(1+7m)$Case $1$: $(m-7)(1-m) = (m+1)(1+7m)$$m - m^2 - 7 + 7m = m + 7m^2 + 1 + 7m$$8m - m^2 - 7 = 7m^2 + 8m + 1$$8m^2 = -8 \Rightarrow m^2 = -1$ (No real solution).Case $2$: $(m-7)(1-m) = -(m+1)(1+7m)$$m - m^2 - 7 + 7m = -(m + 7m^2 + 1 + 7m)$$8m - m^2 - 7 = -7m^2 - 8m - 1$$6m^2 + 16m - 6 = 0$$3m^2 + 8m - 3 = 0$$(3m-1)(m+3) = 0$$m = \frac{1}{3}$ or $m = -3$.Since $m$ is an integer,$m = -3$.

Two equal sides of an isosceles triangle are given by $7x-y+3=0$ and $x+y-3=0$. If the slope $m$ of the third side is an integer,then $m=$

Similar Questions

The area of the quadrilateral formed by the lines $x+2y+3=0$, $2x+4y+9=0$, $x-2y+3=0$, and $3x-6y+11=0$ is

Which one of the following statements is true?

The number of points,having both coordinates as integers,that lie in the interior of the triangle with vertices $(0,0)$,$(0,41)$,and $(41,0)$ is:

If the incentre and the circumcentre of the triangle formed by the lines $x=2$,$4x+3y+7=0$ and $y=3$ are $I$ and $S$ respectively,then $IS=$

$(0, -1)$ and $(0, 3)$ are two opposite vertices of a square. The other two vertices are

Vedclass Test Series

Exam Paper Generator

Online Exam Module