Home
Class 10
MATHS
If the points A(6, 1), B(8, 2), C(9, 4)...

If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.

Text Solution

AI Generated Solution

To find the value of \( p \) such that the points \( A(6, 1) \), \( B(8, 2) \), \( C(9, 4) \), and \( D(p, 3) \) are the vertices of a parallelogram, we can use the property that the diagonals of a parallelogram bisect each other. ### Step-by-Step Solution: 1. **Find the Midpoint of Diagonal AC:** The coordinates of points \( A \) and \( C \) are \( A(6, 1) \) and \( C(9, 4) \). The midpoint \( M_{AC} \) of diagonal \( AC \) can be calculated using the midpoint formula: \[ ...
Promotional Banner

Similar Questions

Explore conceptually related problems

If the points A(6,\ 1),\ \ B(8,\ 2),\ \ C(9,\ 4) and D(k ,\ p) are the vertices of a parallelogram taken in order, then find the values of k and p .

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

If the points A(a ,\ -11),\ \ B(5,\ b),\ \ C(2,\ 15) and D(1,\ 1) are the vertices of a parallelogram A B C D , find the values of a and b .

Of A(-2,-1), B(a ,0), C(4, b) and D(1,2) are the vertices of a parallelogram, find the values of a and b .

Show that the points A(2, 1), B(5, 2). C(6, 4) and D(3, 3) are vertices of a parallelogram. Is this figure a rectangle?

Show that the points A(1,\ 0),\ \ B(5,\ 3),\ \ C(2,\ 7) and D(-2,\ 4) are the vertices of a parallelogram.

If the point (x ,-1),(3, y),(-2,3),a n d(-3,-2) taken in order are the vertices of a parallelogram, then find the values of xa n dydot

Show that the points A(1,\ -2),\ \ B(3,\ 6),\ \ C(5,\ 10) and D(3,\ 2) are the vertices of a parallelogram.

Without using the distance formula, show that the points A (4, 5), B (1, 2), C (4, 3) and D (7, 6) are the vertices of a parallelogram.

If A(-2,-1),B(a ,0),C(4, b)a n d D(1,2) are the vertices f a parallelogram, find the values of a and b