Question

Q 15 The three vertices of a parallelogram are (1,1),(5,5) and (5,8). Find the fourth vertex.
@ve ruide​

Answer 1

The fourth vertex is (1, 13).

Explanation:

Let the fourth vertices be D (a, b).

Let the vertices be A (1, 1), B (5, 5), C (5, 8) and D (a, b).

The diagonals of a parallelogram bisect each other.

So, let's consider O is the midpoint of AC as well as that of BD.

The mid-point of AC is:

Mid-point of AC = ((1 + 5)/2, (1 + 8)/2) = (3, 9/2)

The mid-point of BD is:

Mid-point of BD = ((5 + a)/2, (5 + b)/2)

⇒ (5 + a)/2 = 3

5 + a = 6 ⇒ a = 1

⇒ (5 + b)/2 = 9/2

5 + b = 18 ⇒ b = 13

Thus, the fourth vertex is (1, 13)

Answer 2

Explanation:

1)for this type of question there is one formula (x1+x3-x2),(y1+y3-y2)

2)substitute the values

= (1+5-5), (1+8-5)

=(6-5), (9-5)

=(1,4) is the answer