Question

how to solve this question​

Answer 1

SOLUTION:-

Given:

The parallelogram where coordinates of the three vertices given in order are (-3,2), (-5,-3),(3,-3).

To find:

The coordinates of the fourth vertex of parallelogram.

Explanation:

Let the coordinates of fourth vertex be D (R,M).

We know that, In a ||gm diagonal bisect to each other.

So,

The midpoint of BD= Midpoint of AC.

We have,

Given three vertices of a parallelogram are;

• A(-3,2)
• B(-5,-3)
• C(3,-3)
• D(R,M)

Mid-point of line segment joining the points (R1,M1) & (R2, M2) is;

$( \frac{R1 + R2}{2} , \frac{M1 + M2}{2} )$ Mid-point of AC:

$( \frac{ - 3 + 3}{2} \: \frac{2 - 3}{2} ) \\ \\ ( \frac{0}{2} , \frac{ - 1}{2} )$

Mid-point of BD = Mid-point of AC

Therefore,

Mid-point of BD:

$( \frac{ - 5 + R}{2} \: \frac{ - 3 + M}{2} ) = (\frac{0}{2} \: \frac{ - 1}{2} ) \\ \\ \frac{ - 5 + R}{2} = \frac{0}{2} \\ \\ - 5 + R = 0 \\ \\ R = 5$

&

$\frac{ - 3 + M}{2} = \frac{ - 1}{2} \\ \\ - 3 + M = - 1 \\ \\ M = - 1 + 3 \\ \\ M = 2$

Therefore,

The fourth vertex of ||gm, D is (5,2).