Question

12. The point which divides the line segment of points P(-1, 7) and (4, -3) in the ratio of 2:3 is: (a) (-1,3) (b) (1, -3) (c) (1, -3) (d) (1,3)​

Answer 1

Answer:

Answer is option d) (1,3)   by using section formula

Answer 2

Step-by-step explanation:

Given:P(-1,7) and Q(4,-3)

To find:Find the point which divides the line segment in ratio 2:3 is:

(a) (-1,3)

(b) (1, -3)

(c) (1, -3)

(d) (1,3)

Solution:

Tip: Section formula

If line segment by joining the points $P(x_1,y_1)$and $Q(x_2,y_2)$ is divided by the R(x,y) in m:n ratio,then coordinates of R are given by

$\boxed{\bold{\red{x = \frac{mx_1 + nx_2}{m + n} }}} \\ \\ \boxed{\bold{\green{y = \frac{my_1 + ny_2}{m + n}}}}$

Here,

Points are P(-1,7) and Q(4,-3) ,ratio is 2:3

apply the values in the formula

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

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

$x = \frac{5}{5}$

$\bold{\red{x = 1 }}$

by the same way,find y

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

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

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

$\bold{\green{y = 3 }}$

Coordinates of R are (1,3).

Option D is correct.

Final answer:

Coordinates of R are (1,3).

Option D is correct.

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