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Question
A(3, 0), B(6, 4) and C(−1, 3) are vertices of a triangle ABC. Find length of its median BE.
Sum
Solution
A(3, 0), B(6, 4) and C(−1, 3) are vertices of ΔABC and E on AC
A triangle median is a line segment that links a vertex to the midway of the opposing side.
∴ E is mid-point of AC
Co-ordinate of E
`((-1 + 3)/2, (0 + 3)/2)`
= `(1, 3/2)`
The distance of BE is
BE = `sqrt((6 - 1)^2 + (4 - 3/2)^2)`
= `sqrt(5^2 + (5/2)^2)`
= `sqrt(25 + 25/4)`
= `sqrt(125/4)`
= `(5sqrt5)/2`
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