If the coordinates of the vertices of the tri | vedclass

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

Question

(C) Let the vertices be $A(-1, 6)$,$B(-3, -9)$,and $C(5, -8)$.The median through $C$ passes through $C(5, -8)$ and the midpoint $M$ of $AB$.The midpoi

Vedclass · Accepted Answer

$13x + 14y + 47 = 0$

Vedclass · Answer

(C) Let the vertices be $A(-1, 6)$,$B(-3, -9)$,and $C(5, -8)$.The median through $C$ passes through $C(5, -8)$ and the midpoint $M$ of $AB$.The midpoint $M$ of $AB$ is given by $M = \left( \frac{-1 - 3}{2}, \frac{6 - 9}{2} \right) = \left( -2, -\frac{3}{2} \right)$.The equation of the line passing through $C(5, -8)$ and $M(-2, -\frac{3}{2})$ is given by the two-point form: $y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$.Substituting the values: $y - (-8) = \frac{-\frac{3}{2} - (-8)}{-2 - 5}(x - 5)$.$y + 8 = \frac{-\frac{3}{2} + 8}{-7}(x - 5) \Rightarrow y + 8 = \frac{\frac{13}{2}}{-7}(x - 5)$.$y + 8 = -\frac{13}{14}(x - 5) \Rightarrow 14(y + 8) = -13(x - 5)$.$14y + 112 = -13x + 65 \Rightarrow 13x + 14y + 47 = 0$.

If the coordinates of the vertices of the triangle $ABC$ are $A(-1, 6)$,$B(-3, -9)$,and $C(5, -8)$,then the equation of the median through $C$ is

Similar Questions

If $A(4, -3)$,$B(3, -2)$,and $C(2, 8)$ are the vertices of a triangle,then its centroid will be

In $\Delta ABC$,the coordinates of $B$ are $(0, 0)$,$AB = 2$,$\angle ABC = \frac{\pi}{3}$,and the coordinates of the midpoint of $BC$ are $(2, 0)$. Find the centroid of the triangle.

The orthocentre of the triangle with vertices $\left( 2, \frac{\sqrt{3} - 1}{2} \right)$,$\left( \frac{1}{2}, -\frac{1}{2} \right)$,and $\left( 2, -\frac{1}{2} \right)$ is:

If $(2, 3)$,$(4, 5)$,and $(-2, 11)$ are the vertices of a triangle,what is the distance between the vertex $(4, 5)$ and the circumcenter?

The vertices of $\Delta PQR$ are $P(2, 1)$,$Q(-2, 3)$,and $R(4, 5)$. Find the equation of the median through the vertex $R$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module