Name: Rectangle Formed by Four Points
Uploaded: 2019-07-19
Duration: 5 min 27 s
Description: We know that each of us will have some characteristics. Similarly, in the case of rectangles, too, there are some properties. Let us watch the video and find...

Question

Show that the points

A (4, 3), B (1, 2), C (1, 0)

and

D (4, 1)

are the vertices of a parallelogram and find the lengths of its diagonals.

Accepted Answer

Given: $A (4, 3), B (1, 2), C (1, 0) and D (4, 1)$

To show $A B C D$ is a parallelogram

Finding the mid-point of diagonals $A C, B D$

Using mid-point formula:

Mid-point of $(x_{1}, y_{1}) and (x_{2}, y_{2})$ is $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Mid-point of $A C = (\frac{4 + 1}{2}, \frac{3 + 0}{2}) = (\frac{5}{2}, \frac{3}{2})$

Mid-point of $B D = (\frac{1 + 4}{2}, \frac{2 + 1}{2}) = (\frac{5}{2}, \frac{3}{2})$

We observe that mid-point of $A C =$ Mid-point of $B D$

So, the diagonals bisect each other.

Thus, the given points are the vertices of the parallelogram.

Finding the length of diagonal, we get,

$A C = \sqrt{(1 - 4)^{2} + (0 - 3)^{2}} = \sqrt{9 + 9} = 3 \sqrt{2}$ units

$B D = \sqrt{(4 - 1)^{2} + (1 - 2)^{2}} = \sqrt{9 + 1} = \sqrt{10}$ units

Thus, the lengths of the diagonals are $3 \sqrt{2}$ unit and $\sqrt{10}$ unit.

Show that the points $A (4, 3), B (1, 2), C (1, 0)$ and $D (4, 1)$ are the vertices of a parallelogram and find the lengths of its diagonals.

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

Show that the points A4, 3, B1, 2, C1, 0 and D4, 1 are the vertices of a parallelogram and find the lengths of its diagonals.

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

Show that the points $A (4, 3), B (1, 2), C (1, 0)$ and $D (4, 1)$ are the vertices of a parallelogram and find the lengths of its diagonals.