11. The line $7x – 8y = 4$ divides the join of $(-8, -4)$ and $(6, k)$ in the ratio 2: 5. Find the value of k. - Noon Academy

11. The line $7x - 8y = 4$ divides the join of $(-8, -4)$ and $(6, k)$ in the ratio 2: 5. Find the value of k.

Class 10 | Equation of a Straight Line | Frank | Maths

11. The line $7x - 8y = 4$ divides the join of $(-8, -4)$ and $(6, k)$ in the ratio 2: 5. Find the value of k.

Solution:-

Let us assume the point of intersection of CD and line $7x - 8y = 4$ be the point Q(a, b)

From the question it is given that, line $7x - 8y = 4$ divides the line segment CD are in the ratio 2: 5,

So, CQ: QD $= 2: 5$

So, Point C become $5(-8, -4) = (-40, -20)$

D become $2(6, k) = (12, 2k)$

Then, the coordinates of Q are,

$Q(a, b) = Q[((12 - 40)/7), ((2k - 20)/7)]$

$= Q[-4, ((2k - 20)/7)]$

Since Q(a, b) lies on the line $7x - 8y = 4$ ,

Where, $x = - 4, y = (2k - 20)/7$

$7(-4) - 8((2k - 20)/7) = 4$

$- 28 - (16k - 160)/7 = 4$

$- 196 - 16k + 160 = 28$

$- 36 - 16k = 28$

$16k = - 36 - 28$

$16K = - 64$

$K = -64/16$

$K = -4$

Therefore, value of k is $- 4$ .

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