Question

Find the distance between C(-8,-5) and D(-2,3).
Find the midpoint of CD.

Answer 1

10 units and (- 5, - 1 )

Explanation:

Calculate the distance d using the distance formula

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

with (x₁, y₁ ) = C(- 8, - 5) and (x₂, y₂ ) = D(- 2, 3)

d =
`√((-2+8)^2+(3+5)^2)`

=
`√(6^2+8^2)`

=
`√(36+64)`

=
`√(100)`

= 10

Calculate the midpoint using the midpoint formula

(
`(x_(1)+x_(2) )/(2)`,
`(y_(1)+y_(2) )/(2)` )

=
`(-8-2)/(2)`,
`(-5+3)/(2)` )

=
`(-10)/(2)`,
`(-2)/(2)` )

= (- 5, - 1 )