Question

The three vertices of a parallelogram ABCD, taken in order, A(1,-2), B(3,6) and C(5,10) the coordinates of the fourth vertex D are_____

Answer 1

The Diagonals of a parallelogram bisect each other.

Given parallelogram is ABCD.

The Diagonals will be AC, BD.

Since the Diagonals bisect each other, Their mid points are same.

Given, Vertices of the parallelogram are

A (1, - 2)

B (3, 6)

C ( 5, 10)

Let the fourth Vertex D be (x, y)

Mid point of (a, b) & (h, k) is given by,

( (a + h) /2, (b + k)/2)

So,

Mid point of AC = Mid point of BD

( 1 + 5 /2, - 2 + 10/2) = ( 3+ x/2, 6+y/2)

Comparing X coordinate

⇒ 1 + 5 / 2 = 3 + x / 2

⇒6 = 3 + x

⇒ x = 6 - 3

⇒x = 3

Comparing Y coordinate

⇒-2 + 10 /2 = 6 + y / 2

⇒8 = 6 + y

⇒y = 8 - 6

⇒y = 2

Therefore, The fourth Vertex D is (3,2)

Answer 2

Step-by-step explanation:

x coordinate is3

y coordinate is 2