Question

What are the coordinates of the point which divides the line joining (-1,7) and (4,-3) in the ratio 2:3?

Answer 1

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Answer 2

$\huge {ANSWER}$

Let the two points be A and B.

And the point be P and coordinates of point be x and y.

And let the coordinates of point A be x1 and y1 and of B be x2 and y2.

And the ratio in which they are being divided be m1=2 and m2=3.

A(-1,7)_2_____P(x, y) _____3___B(4,-3)

So, for finding the coordinates of P apply section Formula ,

FOR x,

$x = \frac{m1 \times x1 + m2 \times x2}{m1 + m2}$

$x = \frac{2 \times 4 + 3 \times - 1}{2 + 3}$

$x = \frac{8 - 3}{5}$

$x = 1$

For y,

$y = \frac{m1 \times y2 + m2 \times y2}{m1 + m2}$

$y = \frac{(2 \times - 3) + (3 \times 7)}{2 + 3}$

$y = \frac{ - 6 + 21}{5}$

$y = \frac{15}{5}$

$y = 3$

HENCE THE COORDINATES OF THE POINT JOINING THE LINE WILL BE,

(x, y) = (1,3).