The vertices of Delta PQR are P(2, 1),Q(-2, 3 | vedclass

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

Question

(A) The vertices of $\Delta PQR$ are $P(2, 1)$,$Q(-2, 3)$,and $R(4, 5)$.Let $RL$ be the median through vertex $R$. Therefore,$L$ is the midpoint of $P

Vedclass · Accepted Answer

$3x - 4y + 8 = 0$

Vedclass · Answer

(A) The vertices of $\Delta PQR$ are $P(2, 1)$,$Q(-2, 3)$,and $R(4, 5)$.Let $RL$ be the median through vertex $R$. Therefore,$L$ is the midpoint of $PQ$.Using the midpoint formula,the coordinates of $L$ are $\left(\frac{2 + (-2)}{2}, \frac{1 + 3}{2}\right) = (0, 2)$.The median $RL$ passes through $R(4, 5)$ and $L(0, 2)$.The equation of a line passing through $(x_1, y_1)$ and $(x_2, y_2)$ is $y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$.Substituting the points $(4, 5)$ and $(0, 2)$:$y - 5 = \frac{2 - 5}{0 - 4}(x - 4)$$y - 5 = \frac{-3}{-4}(x - 4)$$4(y - 5) = 3(x - 4)$$4y - 20 = 3x - 12$$3x - 4y + 8 = 0$.

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 $R$.

Similar Questions

The centroid of a triangle,whose vertices are $(2, 1)$,$(5, 2)$,and $(3, 4)$,is

The orthocentre of the triangle formed by lines $x+y+1=0$,$x-y-1=0$,and $3x+4y+5=0$ is

Two vertices of a triangle are $(5, -1)$ and $(-2, 3)$. If the orthocentre is the origin,then the coordinates of the third vertex are:

The vertices of a triangle are at $-\hat{i}+3 \hat{j}$ and $2 \hat{i}+5 \hat{j}$ and its orthocenter is at $\hat{i}+2 \hat{j}$. If the position vector of the third vertex is $a \hat{i}+b \hat{j}$,then $(a, b)=$

If the vertices of a triangle are $(-2,3), (6,-1)$ and $(4,3)$,then the coordinates of the circumcentre of the triangle are

Vedclass Test Series

Exam Paper Generator

Online Exam Module