Question

A (5a + 2, b + 6) divides the line segment joining B (4, - 3a) and C (8a, 5) internally in the ratio 3: 1, then find the values of a and b

Answer 1

Step-by-step explanation:

I hope it's helpful to you

Answer 2

Step-by-step explanation:

Given:A (5a + 2, b + 6) divides the line segment joining B (4, - 3a) and C (8a, 5) internally in the ratio 3: 1.

To find:Find the values of a and b.

Solution:

We know that section formula is given by

$x = \frac{mx_1 + nx_2}{m + n} \\ \\ y = \frac{my_1 + ny_2}{m + n}$

Here,

A divides the line.

Thus,coordinates of points are (5a+2,b+6)

B(4,-3a)____3______(A)___1___c(8a,5)

apply section formula,for x coordinate to find value of a

$5a + 2 = \frac{3 \times 8a + 1 \times 4}{3 + 1} \\ \\ 5a + 2 = \frac{24a + 4}{4} \\ \\ 4(5a + 2) = 24a + 4 \\ \\ 20a + 8 = 24a + 4 \\ \\ 20a - 24a = 4 - 8 \\ \\ - 4a = - 4 \\ \\ \bold{a = 1}$

find b using y Coordinates

$b + 6 = \frac{5 \times 3 + 1 \times ( - 3a)}{3 + 1} \\ \\ b + 6 = \frac{15 - 3a}{4} \\ \\ 4(b + 6) = 15 - 3a \\ \\ 4b + 24 = 15 - 3(1) \\ \\ 4b = 12 - 24 \\ \\ 4b = - 12 \\ \\ \bold{b = - 3}$

Final answer:

Value of a=1 and b=-3.

Hope it helps you.

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