$A (4, 2), B (6, 5)$ and $C (1, 4)$ are the vertices of $\triangle ABC$.The median from A meets BC in D. Find the coordinates of the point D.
Given:
$A (4, 2), B (6, 5)$ and $C (1, 4)$ are the vertices of $\triangle ABC$.
The median from A meets BC in D.
To do:
We have to find the coordinates of point D.
Solution:
$D$ is the mid-point of BC.
![](/assets/questions/media/158630-42982-1617901815.jpg)
This implies,
Using mid-point formula, we get,
Coordinates of $D=(\frac{6+1}{2}, \frac{5+4}{2})$
$=(\frac{7}{2},\frac{9}{2})$
The coordinates of the point $D$ are $(\frac{7}{2},\frac{9}{2})$ .
- Related Articles
- The points $A (x_1, y_1), B (x_2, y_2)$ and $C (x_3, y_3)$ are the vertices of $\triangle ABC$.The median from $A$ meets $BC$ at $D$. Find the coordinates of the point $D$.
- $A (4, 2), B (6, 5)$ and $C (1, 4)$ are the vertices of $\triangle ABC$.Find the coordinates of point P on AD such that $AP : PD = 2 : 1$.
- Find the area of a quadrilateral $ABCD$, the coordinates of whose vertices are $A (-3, 2), B (5, 4), C (7, -6)$ and $D (-5, -4)$.
- The points \( A\left(x_{1}, y_{1}\right), \mathrm{B}\left(x_{2}, y_{2}\right) \) and \( \mathrm{C}\left(x_{3}, y_{3}\right) \) are the vertices of \( \Delta \mathrm{ABC} \)The median from \( \mathrm{A} \) meets \( \mathrm{BC} \) at \( \mathrm{D} \). Find the coordinates of the point \( \mathrm{D} \).
- ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is(a) 2 :1(b) 1:2(c) 4:1(d) 1:4
- Let $A(4, 2), B(6,5)$ and $C(1, 4)$ be the vertices of $∆ABC$.(i) The median from $A$ meets $BC$ at $D$. Find the coordinates of the point $D$.(ii) Find the coordinates of the point $P$ on $AD$, such that $AP : PD = 2 : 1$.(iii) Find the coordinates of points $Q$ and $R$ on medians $BE$ and $CF$ respectively, such that $BQ : QE = 2 : 1$ and $CR : RF = 2 : 1$.(iv) What do you observe?[Note: The point which is common to all the three medians is called centroid and this point divides each median in the ratio 2: 1](v) If $A(x_1, y_1), B(x_2, y_2)$ and $C(x_3, y_3)$ are the vertices of $∆ABC$, find the coordinates of the centroid of the triangles.
- Prove that the points $A (1, 7), B (4, 2), C (-1, -1)$ and $D (-4, 4)$ are the vertices of a square.
- If $A (-1, 3), B (1, -1)$ and $C (5, 1)$ are the vertices of a triangle ABC, find the length of the median through A.
- Find the area of the quadrilaterals, the coordinates of whose vertices are$(-3, 2), (5, 4), (7, -6)$ and $(-5, -4)$
- Find the area of quadrilateral ABCD, whose vertices are: $A( -3,\ -1) ,\ B( -2,\ -4) ,\ C( 4,\ -1)$ and$\ D( 3,\ 4) .$
- Find the area of a triangle whose vertices are$(1, -1), (-4, 6)$ and $(-3, -5)$
- Show that the points $A (5, 6), B (1, 5), C (2, 1)$ and $D (6, 2)$ are the vertices of a square.
- Find the area of the quadrilaterals, the coordinates of whose vertices are$(1, 2), (6, 2), (5, 3)$ and $(3, 4)$
- Show that $A (-3, 2), B (-5, -5), C (2, -3)$ and $D (4, 4)$ are the vertices of a rhombus.
- If the coordinates of the mid-points of the sides of a triangle are $(3, 4), (4, 6)$ and $(5, 7)$, find its vertices.
Kickstart Your Career
Get certified by completing the course
Get Started