Let $A(4,2)$,$B(6,5)$,and $C(1,4)$ be the vertices of $\Delta ABC$. The median from $A$ meets $BC$ at $D$. Find the coordinates of the point $D$.
(N/A) The median $AD$ of the triangle divides the side $BC$ into two equal parts.
Therefore,$D$ is the mid-point of side $BC$.
The coordinates of the mid-point of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ are given by $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$.
Here,$B = (6, 5)$ and $C = (1, 4)$.
Coordinates of $D = \left(\frac{6+1}{2}, \frac{5+4}{2}\right) = \left(\frac{7}{2}, \frac{9}{2}\right)$ or $(3.5, 4.5)$.
Therefore,$D$ is the mid-point of side $BC$.
The coordinates of the mid-point of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ are given by $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$.
Here,$B = (6, 5)$ and $C = (1, 4)$.
Coordinates of $D = \left(\frac{6+1}{2}, \frac{5+4}{2}\right) = \left(\frac{7}{2}, \frac{9}{2}\right)$ or $(3.5, 4.5)$.
Explore More
Similar Questions
If the points are $(12, 10)$ and $(0, 8)$, then the midpoint of the line segment joining these two points is $\ldots \ldots \ldots \ldots$
Easy
View Solution$P$ is a point on $\overline{AB}$ such that $A - P - B$. $A(x_{1}, y_{1})$ and $B(x_{2}, y_{2})$ are the given points. If point $P$ divides $\overline{AB}$ from $A$ in the ratio $m : n$ (where $\frac{m}{n} > 0$),then the coordinates of $P$ are:
Easy
View Solution$A (1, -2)$ and $B (-7, 1)$ are the given points. Find $P$ on the line segment $AB$ such that $P$ lies on the extension of $AB$ (as indicated by $P-A-B$ order,though the condition $3AP = 5AB$ implies $P$ is outside the segment $AB$) and $3AP = 5AB$.
Medium
View SolutionFind the coordinates of the point $R$ on the line segment joining the points $P(-1, 3)$ and $Q(2, 5)$ such that $PR = \frac{3}{5} PQ$.
Medium
View SolutionIn which ratio does the $X$-axis divide the line segment joining $A(1, 2)$ and $B(4, -5)$ starting from $A$?
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo