Question

in what ratio does the point (-4,6) divide the line segment joining the points A(-6,10) and B (3,8)
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Answer 1

Answer:

2:7

Step-by-step explanation:

Let P(-4,6) divided AB in the ratio k : 1.

Here, (x₁,y₁) = (-6,10), (x₂,y₂) = (3,8), m = k, n = 1.

Section formula:

Coordinates of P = (3k - 6/k + 1, -8k + 4/k + 1)

⇒ (-4,6) = (3k - 6/k + 1, -8k + 4/k + 1).

So,

⇒ -4 = (3k - 6)/(k + 1)

⇒ -4(k + 1) = 3k - 6

⇒ -4k - 4 = 3k - 6

⇒ -4k - 3k = -6 + 4

⇒ -7k = -2

⇒ k = 2/7.

Therefore, the ratio is 2:7.

Hope it helps!

Answer 2

Step-by-step explanation:

Let the point (-4,6) be M and the ratio in which it divides the line segment be k:1

By section formula the coordinates of the point M are

(-6+3k/k+1,10-8k/k+1)

But M is (-4,6)

-6+3k/k+1=-4

7k=2

k=2/7

Therefore the ratio is 2:7