Help with geometry work!?

Question

Use distance formula to find out whether HM is congruent with ML
1) H(-1,3)
M(1,7)
L(3,3)
2) H(-5,2)
M(-4,6)
L(-6,2)

Answer 1

Two line segments are congruent if they have the same length.

1)H(-1,3) = (x1,y1)

M(1,7) = (x2,y2)

Distance between HM =√ [(x2-x1)^2+(y2-y1)^2]

=√(1-(-1))^1+(7-3)^2

=√(1+1)^2+4^2

=√4+16 = √20

M(1,7)  = (x1,y1)

L(3,3) = (x2,y2)

Distance between ML =√(3-1)^2+(3-7)^2

=√2^2+(-4)^2

=√4+16 = √20

HM =ML then HM is congruent to ML

2)H(-5,2) M(-4,6) L(-6,2)

Distance between HM =√(-4-(-5))^2+(6-2)^2

= √1+16 = √17

Distance between ML = √(-6-(-4))^2+(2-6)^2

=√(-6+4)^2+(-4)^2

= √4+16 = √20

HM is not equal to ML, HM is not congruent to ML.