Question

the point a(1,-2),B(2,3),C(K,2)and D(-4,-3)are the vertice of parallelogram .find the value of K

Answer 1

hi here is ur answer

Answer 2

Answer:

k = -3

Step-by-step explanation:

Our question: the point a(1,-2),B(2,3),C(K,2)and D(-4,-3)are the vertice of parallelogram .find the value of K.

We know that the points given are A(1, -2), B(2, 3), C(k, 2), D(-4, -3).

It is a fact that diagonals of parallelograms bisect each other.

Hence:

1. lets compute the mid-point of AC, we have:

A = (1,-2) and C = (k,2).

Then:

⇒ $(\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )$

⇒ $(\frac{1+k}{2}, 0)$

2. lets compute the mid-point of BD, we have:

B = (2,3) and D = (-4,-3)

Then:

⇒ $(\frac{x_{1} +x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )$

⇒ $(-1, 0)$

Now, if we compare both points we have that the coordinates of the first one must be equal to the second one, then:

⇒ (1 + k)/2 = -1

⇒ 1 + k = -2

⇒ k = -3.

Therefore, the value of k = -3.