Question

Determine whether The given segments have the same length. Justify your answer

Answer 1

We know the distance formula is

$\sqrt{ (x_{2}-x_{1})^2+ (y_{2}-y_{1})^2 }$

9)

Here A( -4,2) and B(1,4)

So length of AB

= $\sqrt{(1-(-4))^2+(4-2)^2} =\sqrt{5^2+2^2} =\sqrt{29}$

Also C(2,1)

Length of BC

= $\sqrt{(2-1)^2+(-1-4)^2} =\sqrt{1^2+(-5)^2} =\sqrt{26}$

So we can see that length of AB is not equal to length of BC

11.

Now AB = $\sqrt{29}$

Also C(2,-1) & D(4,4)

Length of CD

= $\sqrt{(4-2)^2+(4-(-1)) ^2} =\sqrt{2^2+5^2} =\sqrt{29}$

Yes AB = CD