Question

Could someone help me find the length of each segment and which statements are true?

Answer 1

see explanation

Explanation:

(a)

calculate the lengths using the distance formula

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK =
`√((3-(-3))^2+(-8-(-7))^2)`

=
`√((3+3)^2+(-8+7)^2)`

=
`√(6^2+(-1)^2)`

=
`√(36+1)`

=
`√(37)`

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN =
`√((7-8)^2+(-3-3)^2)`

=
`√((-1)^2+(-6)^2)`

=
`√(1+36)`

=
`√(37)`

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ =
`√(-2-(-8))^2+(2-1)^2)`

=
`√((-2+8)^2+1^2)`

=
`√(6^2+1)`

=
`√(36+1)`

=
`√(37)`

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true