Question

Find the ratio in which the point (a, 7) divides the line segment AB given A(-5, 6) and B(4, 10). Also, find the value of a.​

Answer 1

Step-by-step explanation:

A( -5, 6). B(4, 10)

Let the point P(a , 7) devides internally in the ratio k : 1

By section formula

(a, 7) = [4k - 5/ k + 1 , 10k + 6/ k+1]

4k - 5/ k + 1 = a and 10k + 6/ k+1 = 7

10k + 6 = 7k + 7

3k = 1

k = 1/3

∴ division ratio is 1 : 3

a = [4(1/3) - 5] / [ 1/3 + 1]

= (4 - 15) /4

= - 11/4

Answer 2

Answer:

The value of a is

$\sf \: \dfrac{ - 11}{4}$

Step-by-step explanation:

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