## find the equation of the median from b in ABC whose vertices are (1,5), B(5,3) and C(-3, -2)

Question

find the equation of the median from b in ABC whose vertices are (1,5), B(5,3) and C(-3, -2)

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1 week 2021-07-22T04:32:07+00:00 1 Answers 2 views 0

y = x + 6

x = 1

y = ¼(x – 5) + 3

Step-by-step explanation:

Vetices are;

A(1,5), B(5,3) and C(-3, -2)

Thus;

Median of AB is; D = (1 + 5)/2, (5 + 3)/2

D = (3, 4)

Median of BC is; E = (5 + (-3))/2, (3 + (-2))/2

E = (1, 0.5)

Median of AC is; F ; (-3 + 1)/2, (-2 + 5)/2

F = (-1, 1.5)

Thus, the median lines will be;

CD, AE & BF.

Thus;

Equation of CD is;

(y – (-3))/(x – (-2)) = (-2 – 4))/(-3 – 3)

(y + 4)/(x + 2) = -6/-6

y – 4 = 1(x + 2)

y = 4 + x + 2

y = x + 6

Equation of AE;

(y – 5)/(x – 1) = (0.5 – 5)/(1 – 1)

(y – 5)/(x – 1) = -4.5/0

Cross multiply to get;

0(y – 5) = -4.5(x – 1)

-4.5x = -4.5

x = 1

Equation of BF;

(y – 3)/(x – 5) = (1.5 – 3)/(-1 – 5)

(y – 3)/(x – 5) = -1.5/-6

(y – 3)/(x – 5) = 1/4

y – 3 = ¼(x – 5)

y = ¼(x – 5) + 3