Question

Show that the points A(-1,-2),B(1,0),C(-1,2),D(3,0) are the vertices of a square

Answer 1

Given:

A(-1, -2) =Let (x1, y1)

B(1, 0) =Let (x2, y2)

C(-1, 2) = Let (x3, y3)

D(3, 0) =Let (x4, y4)

To Show:

Given points are the vertices of a square.

Solution:

By distance formula,

d(A, B) =√(y2-y1) ²+(x2-x1) ²

d(A, B) =√(0+2) ²+(1+1) ²

d(A, B) =2√2............ (1)

d(B, C) =√(y3-y2) ²+(x3-x2) ²

d(B, C) =√(2) ²+(-1-1) ²

d(B, C) =2√2............... (2)

d(C, D) =√(y4-y3) ²+(x4-x3) ²

d(C, D) =√(-2) ²+(3+1) ²

d(C, D) =√4+16=2√5............ (3)

d(A, D) =√(y4-y1) ²+(x4-x1) ²

d(A, D) =√(2) ²+(4) ²

d(A, D) =2√5............. (4)

As we know that All sides of a square are congruent .

But from (1) , (2), (3), (4)

All sides are not congruent,

So the given points are not the vertices of a square

Answer 2

Step-by-step explanation:

by using distance formula