Question

What is the length of the line segment joining the points (-1, 4) and (2 , -5)?

a. 3√2
b. 3√10
c. √2
d. √10

Answer 1

Given: Points (-2,-3) and (1,4)

Find: Length of Segment

Plan: Use Distance Formula

Let Distance = D = √[(x1 - x2)^2 + (y1 - y2)^2]

D = √[(-2 -1)^2 + (-3 -4)^2] = √[(-3)^2 + (-7)^2] =

√(9 + 49) = √(58) units or ≈ 7.62 units rounded ✅

Double Check: Reasonable/Recalculated ✅ ✅

Answer: √(58) units or ≈ 7.62 units rounded

Answer 2

b

Explanation:

calculate the length using the distance formula

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

with (x₁, y₁ ) = (- 1, 4 ) and (x₂, y₂ ) = (2, - 5 )

d =
`√((2-(-1))^2+(-5-4)^2)`

=
`√((2+1)^2+(-9)^2)`

=
`√(3^2+81)`

=
`√(9+81)`

=
`√(90)`

=
`√(9(10))`

=
`√(9)` ×
`√(10)`

= 3
`√(10)`