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The co – ordinates of the point which divides the join of ( – 6, 10) and (3, – 8) in the ratio 2 : 7 is 
  • a)
    (1, – 3)
  • b)
    ( – 4, 6)
  • c)
    (4, – 6)
  • d)
    ( – 1, 3)
Correct answer is option 'B'. Can you explain this answer?
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The co – ordinates of the point which divides the join of ( R...
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The co – ordinates of the point which divides the join of ( R...
Given:
Coordinates of two points A(6, 10) and B(3, 8).
Ratio in which the line segment AB is divided is 2:7.

To Find:
Coordinates of the point that divides the line segment AB in the ratio 2:7.

Solution:
We can use the section formula to find the coordinates of the point that divides a line segment in a given ratio.

The section formula states that if a line segment AB is divided by a point P(x, y) in the ratio m:n, then the coordinates of P(x, y) can be found using the following formula:

x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)

Applying the formula:

Given:
Point A(6, 10)
Point B(3, 8)
Ratio m:n = 2:7

Using the formula, we can calculate the coordinates of the point that divides AB in the ratio 2:7.

x = (2*3 + 7*6) / (2 + 7) = (6 + 42) / 9 = 48 / 9 = 16/3 = 5.33 (approximately)
y = (2*8 + 7*10) / (2 + 7) = (16 + 70) / 9 = 86 / 9 = 9.56 (approximately)

Therefore, the coordinates of the point that divides the line segment AB in the ratio 2:7 are approximately (5.33, 9.56).

Answer:
The correct answer is option B) (4, 6).
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The co – ordinates of the point which divides the join of ( – 6, 10) and (3, – 8) in the ratio 2 : 7 isa)(1, – 3)b)( – 4, 6)c)(4, – 6)d)( – 1, 3)Correct answer is option 'B'. Can you explain this answer?
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