Question

Find the ratio in which the point (4,8) divides the line segment joining the points
(8,6) and (0,10)
a) 1:1 b) 1:2 c) 2:1 d) 3:1​

Answer 1

Answer:

a) 1:1

hope It helps u

Answer 2

$\huge\rm\underline \blue{Solution:-}$

Let the ratio be k:1

• Let Coordinates of A be A(8,6)
• Let Coordinates of B be B(0,10)

And coordinates of p = P(4,8)

• By section formula

$\bf\:(x,y)= \pink{(\dfrac{mx_2+n+x_1}{m+n},\dfrac{my_2+ny_1}{m+n})}$

The Coordinates of p are :-

• Let m = k and n = 1

$\longmapsto\rm\:p (\frac{k \times 0 + 1 \times 8}{k + 1} \: ,\: \frac{k \times 10 +1 \times 6 }{k + 1}) \\ \\ \longmapsto\rm\:p( \frac{8}{k + 1} \: , \: \frac{10k + 6}{k + 1}) \\ \\ \rm \: \: cordinates \: of \: p \: are \: p(4,8) \\ \\ \: \: \: \: \: \: \bf\: \underline{ \: \: case \: 1st : \: \: \: } \\ \\\longmapsto\rm\: \frac{8}{k + 1} = 4 \\ \\ \longmapsto\rm\:8 = 4k + 4 \\ \\ \longmapsto\rm\:4k = 4 \\ \\ \longmapsto\bf\:k = 1 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \underline{ \: \: case \: 2nd : \: \: } \\ \\ \longmapsto\rm\: \frac{10k + 6}{k + 1} = 8\\ \\\longmapsto\rm\:10k + 6 = 8k + 8 \\ \\ \longmapsto\rm\:2k = 2 \\ \\ \longmapsto\bf\:k = 1$

• k = 1 in each case .

So, The required ratio is 1:1.

Hence p divides line segment AB in the ratio of 1:1.

• Option 1 is correct ✔️