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Question

A (5, 4), B (-3, -2) and C (1, -8) are the vertices of a triangle ABC. Find :

(i) the slope of the altitude of AB,

(ii) the slope of the median AD and

(iii) the slope of the line parallel to AC.


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Solution

Given, A (5, 4), B (-3, -2) and C (1, -8) are the vertices of a triangle ABC.

(i) Slope of AB = fraction numerator negative 2 minus 4 over denominator negative 3 minus 5 end fraction equals 3 over 4

Slope of the altitude of AB = fraction numerator negative 1 over denominator s l o p e space o f space A B end fraction equals fraction numerator negative 4 over denominator 3 end fraction

(ii) Since, D is the mid-point of BC.

Co-ordinates of point D are

open parentheses fraction numerator negative 3 plus 1 over denominator 2 end fraction comma fraction numerator negative 2 minus 8 over denominator 2 end fraction close parentheses equals open parentheses negative 1 comma negative 5 close parentheses

Slope of AD = fraction numerator negative 5 minus 4 over denominator negative 1 minus 5 end fraction equals 3 over 2

(iii) Slope of AC = fraction numerator negative 8 minus 4 over denominator 1 minus 5 end fraction equals 3

Slope of line parallel to AC = Slope of AC = 3


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