Question

If (3,a) lies on the line joining (1,-4) and (-2,5).Find a

Answer 1

The value of "a" is -10

Solution:

If the point P(3, a) lies on the line segment joining the point A(1, -4) and B(-2, 5), then all these points are collinear and the slopes AB, AP, PB are same

The slope is given by formula:

$m = \frac{ y_2- y_1}{x_2-x_1}$

Slope of AB is:

A = (1, -4)

B = (-2, 5)

$m = \frac{ 5 + 4 }{-2 - 1 }$

$m = \frac{9}{-3}\\\\m = -3$

The slope of PB:

P = (3, a)

B = (-2, 5)

$m = \frac{5 - a}{-2 - 3}\\\\m = \frac{5-a}{-5}$

Both the slopes are equal

$-3 = \frac{ 5 - a }{-5}\\\\15 = 5 - a\\\\a = -10$

Then the value of "a" is -10

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