Math, asked by joshua9884, 8 months ago

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​

Answers

Answered by manish2293
8

Answer:

a) 1:1

hope It helps u

Attachments:
Answered by Anonymous
22

 \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 ✔️
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