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Example Question #21 : Distance Formula
Find the length of a line segment whose endpoints are located at the coordinates and
.
According to the distance formula, the linear distance between two points
and
is given by
,
which is a generalization of the Pythagorean Theorem for any two points on the coordinate plane.
The two points given in this problem are and
. Although the question asks for the length of a line segment given its two endpoints, the distance formula is applicable here because the geometric meaning of "distance between two points" is the length of a line segment. Hence, we can use the distance formula to determine the distance between these two endpoints as shown:
Hence, the line segment bounded by the points and
is
units long.
Example Question #21 : Distance Formula
One line has four collinear points in order from left to right A, B, C, D. If AB = 10’, CD was twice as long as AB, and AC = 25’, how long is AD?
45'
35'
30'
40'
50'
45'
AB = 10 ’
BC = AC – AB = 25’ – 10’ = 15’
CD = 2 * AB = 2 * 10’ = 20 ’
AD = AB + BC + CD = 10’ + 15’ + 20’ = 45’
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