Question

बिंदुओं (-4, 5) तथा (0, -10) को जोड़ने वाले रेखाखंड को बिन्दु (x, 0) निम्न अनुपात में विभाजित करता है :

(A) 1:3

(B) 2:1

(C) 1:1

(D) 1:2

Answer 1

सही विकल्प है: (D) 1 : 2

According to the Section formula, if a point P(x, y) that lies on a line Segment AB joining points \(A(x_{1}, y_{1})\) and \(B(x_{2}, y_{2})\) divides the line in the ratio m : n, then the Coordinates can be.

Coordinates = (x, y) = \(\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)\).

Let the point P(x, 0) divide the segment joining A(- 4, 5) and B(0, - 10) in the ratio m : n, then

(x, 0) = \(\left(\frac{m \times 0 +n(-4)}{m+n}, \frac{m(-10)+n(5)}{m+n}\right)\) 

0 = \(\frac{-10m+5n}{m+n}\)

-10m + 5n = 0

-10m = -5n

\(\frac{m}{n} = \frac{5}{10}\)  

\(\frac{m}{n} = \frac{1}{2}\)

m : n = 1 : 2

Answer 2

सही विकल्प है: (D) 1:2