What is the length of the segment with endpoints (0,-1)(0,−1) and (4, 7)(4,7)?

1 Answer
Alan P.
Jun 26, 2018

Length from (0,-1) to (4,7): color(blue)(4sqrt(5))4√5

Explanation:

The horizontal distance, DeltaxΔx, between (0,-1)(0,−1) and (4,7)(4,7) is abs(4-0)=4|4−0|=4
The vertical distance, DeltayΔy, between (0,-1)(0,−1) and (4,7)(4,7) is abs(7-(-1))=8|7−(−1)|=8

Based on the Pythagorean Theorem the distance between the two points is
color(white)("XXX")sqrt(4^2+8^2)=sqrt(4^2 * (1+2^2))=4sqrt(5)XXX√42+82=√42⋅(1+22)=4√5

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