Question

Find the distance BF for the points B(1, –1) and F(–3, 5).

Answer 1

You know the song, "I Love Rock n' Roll"?

Remember these catchy lyrics that go to the tune to that song's chorus...

Dis-tance formula!
Subtract the X's, Subtract the Y's
Dis-tance formula!
Square root of the sum of squares!

This forms this pretty little equation...

D(x, y) = √((x2 - x1)^2 + (y2 - y1)^2)

Plug in your values and solve.

B(1, -1) --> (x1, y1)
F(-3, 5) --> (x2, y2)

x1 = 1
x2 = -3
y1 = -1
y2 = 5

D(x, y) = √((-3 - 1)^2 + (5 - -1)^2)
D(x, y) = √((-4)^2 + (6)^2)
D(x, y) = √(16 + 36)
D(x, y) = √(52)
D(x, y) = √(13*4)
D(x, y) = √(13) * √(4)
D(x, y) = 2√(13)

The distance between points B and F is equal to exactly 2√(13) units, which is roughly 7.21111111 units of length.