Question

three consecutive vertices of a parallelogram ABCD are A (1,2),B (1,0),C(4,0). Find the fourth vertex

Answer 1

Here is your answer buddy,

Given: ABCD is a parallelogram.

Let vertex of D is (x, y) and O is the mid-point of AC and BD

Since, the diagonals of a parallelogram bisect each other.

Therefore,

Coordinates of the mid-point of AC = coordinates of mid-point of BD

Now,

$\frac{1+4}{2}, \frac{0+2}{2}$ = $\frac{1+x}{2}, \frac{0+y}{2}$

=> $\frac{5}{2}, \frac{2}{2}$ = $\frac{1+x}{2}, \frac{y}{2}$

Therefore,

$\frac{5}{2}$ = $\frac{1+x}{2}$

=> 10 = 2 + 2x ( by cross multiplication)
=> 8 = 2x
=> x = 4

Again,

$\frac{y}{2}$ = 1

=>y = 2

So the fourth vertex is ( 4,2 )

Hope this helps you.
Be Brainly.

Answer 2

Answer:

Step-by-step explanation:

Here is your answer buddy,

Given: ABCD is a parallelogram.

Let vertex of D is (x, y) and O is the mid-point of AC and BD

Since, the diagonals of a parallelogram bisect each other.

Therefore,

Coordinates of the mid-point of AC = coordinates of mid-point of BD

Now,

=

=>  =

Therefore,

=

=> 10 = 2 + 2x ( by cross multiplication)

=> 8 = 2x

=> x = 4

Again,

= 1

=>y = 2

So the fourth vertex is ( 4,2 )

Hope this helps you.

Be Brainly.

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