Question

using section formula show that the points A(1,0),B(5,3),C(2,7),D(-2,4) are the vertices of parallelogram taken in order.

Answer 1

This is the answer. Hope it will be helpful.

Answer 2

Answer:

The proof is given below.

Step-by-step explanation:

Given vertices of parallelogram, A(1,0),B(5,3),C(2,7),D(-2,4)

We have to define the order of vertices of parallelogram

If AC and BD are diagonal then the above given order is correct. Hence, by Section formula we prove that AC and BD are diagonal.

As diagonal of parallelogram bisect each other hence, we can find the coordinates of intersection of diagonal from both the diagonal.

Mid-point of AC is $(\frac{1+2}{2},}{\frac{0+7}{2}})=(\frac{3}{2},\frac{7}{2})$

Mid-point of BD is $(\frac{5-2}{2},}{\frac{3+4}{2}})=(\frac{3}{2},\frac{7}{2})$

From above the mid point above two sides are same. Hence, these AC and BD must be diagonal.

⇒ Given order of vertices of parallelogram A(1,0),B(5,3),C(2,7),D(-2,4) is correct