Question

.The points 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:

(d) (1,3)

Step-by-step explanation:

let the point which devides the line segment be (x,y)

By section formula,

if a point (x,y) divides a line segment through the points (

(x1,y1) and (x2,y2) in the ratio m1 :m2 , then

$(x,y) = ( \frac{m1 \: x2 \: + m2 \: x1}{m1 \: + \: m2} \: \: , \frac{m1y2 + \: m2y1}{m1 + m2} )$

Here , x1 = -1 , x2 = 4

y1 = 7 , y2 = -3

m1 = 2 , m2 = 3

So,

$(x,y) = ( \frac{2 \times \: 4 \: + 3 \times \: - 1}{2 \: + \: 3} \: \: , \frac{2 \times - 3 + \: 3 \times 7}{2 + 3} ) \\ = ( \frac{8 - 3}{5} \: , \frac{ - 6 + 21}{5} ) \\ = (1,3)$

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.

(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.

Hope it helps you.

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