The quadratic equation whose roots are the co | vedclass

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

Question

(C) Let the vertices be $A(-2,-1)$,$B(6,-1)$,and $C(2,5)$.First,find the perpendicular bisector of $AB$. Since $A$ and $B$ have the same $y$-coordinat

Vedclass · Accepted Answer

$3x^2-8x+4=0$

Vedclass · Answer

(C) Let the vertices be $A(-2,-1)$,$B(6,-1)$,and $C(2,5)$.First,find the perpendicular bisector of $AB$. Since $A$ and $B$ have the same $y$-coordinate,the line $AB$ is horizontal. The midpoint is $(\frac{-2+6}{2}, -1) = (2,-1)$. The perpendicular bisector is the vertical line $x=2$ ... $(i)$.Next,find the perpendicular bisector of $BC$. The midpoint of $BC$ is $(\frac{6+2}{2}, \frac{-1+5}{2}) = (4,2)$. The slope of $BC$ is $m = \frac{5-(-1)}{2-6} = \frac{6}{-4} = -\frac{3}{2}$. The slope of the perpendicular bisector is $\frac{2}{3}$. The equation is $y-2 = \frac{2}{3}(x-4)$ $\Rightarrow 3y-6 = 2x-8$ $\Rightarrow 2x-3y=2$ ... (ii).Substitute $x=2$ from $(i)$ into (ii): $2(2)-3y=2$ $\Rightarrow 4-3y=2$ $\Rightarrow 3y=2$ $\Rightarrow y=\frac{2}{3}$.The circumcentre is $(2, \frac{2}{3})$.The quadratic equation with roots $2$ and $\frac{2}{3}$ is $x^2 - (2+\frac{2}{3})x + 2(\frac{2}{3}) = 0$.$x^2 - \frac{8}{3}x + \frac{4}{3} = 0 \Rightarrow 3x^2-8x+4=0$.Thus,option $(c)$ is correct.

The quadratic equation whose roots are the coordinates of the circumcentre of the triangle formed by the points $(-2,-1), (6,-1),$ and $(2,5)$ is

Similar Questions

Let $PS$ be the median of the triangle with vertices $P(2,2)$,$Q(6,-1)$,and $R(7,3)$. The equation of the line passing through $(1,-1)$ and parallel to $PS$ is:

Find the orthocenter of the triangle with vertices $(8, -2)$,$(2, -2)$,and $(8, 6)$.

Let the area of a $\triangle PQR$ with vertices $P(5, 4)$,$Q(-2, 4)$,and $R(a, b)$ be $35$ square units. If its orthocenter and centroid are $O\left(2, \frac{14}{5}\right)$ and $C(c, d)$ respectively,then $c+2d$ is equal to:

The orthocentre of the triangle whose vertices are $(0, 0)$,$(2, -1)$,and $(1, 3)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module