If the vertices of a triangle are A(1, 4),B(3 | vedclass

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

Question

(A) The median passing through vertex $C$ connects $C$ to the midpoint of the opposite side $AB$.Let $M$ be the midpoint of $AB$. The coordinates of $

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) The median passing through vertex $C$ connects $C$ to the midpoint of the opposite side $AB$.Let $M$ be the midpoint of $AB$. The coordinates of $M$ are given by the midpoint formula: $M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{1 + 3}{2}, \frac{4 + 0}{2} \right) = (2, 2)$.The length of the median is the distance between $C(2, 1)$ and $M(2, 2)$.Using the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$,we get:$d = \sqrt{(2 - 2)^2 + (2 - 1)^2} = \sqrt{0^2 + 1^2} = \sqrt{1} = 1$.

If the vertices of a triangle are $A(1, 4)$,$B(3, 0)$,and $C(2, 1)$,then the length of the median passing through $C$ is

Similar Questions

The incentre of the triangle formed by the straight lines $y=\sqrt{3}x$,$y=-\sqrt{3}x$ and $y=3$ is

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

If the coordinates of the vertices of triangle $ABC$ are $(6, 0)$,$(0, 6)$,and $(7, 7)$ respectively,find the circumcenter of the triangle.

If the vertices of a triangle are $(a, b - c)$,$(b, c - a)$,and $(c, a - b)$,then the centroid of the triangle lies

Show that the area of the triangle formed by the lines $y=m_{1}x+c_{1}$,$y=m_{2}x+c_{2}$ and $x=0$ is $\frac{(c_{1}-c_{2})^{2}}{2|m_{1}-m_{2}|}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module