Question

The point which divides the line segment joining the points (2,-2) and (-14, 6) in the ratio 3 : 5 internally, lies in quadrant (a) (b) || (C) III (d) IV​

Answer 1

SOLUTION

CORRECT QUESTION

TO CHOOSE THE CORRECT OPTION

The point which divides the line segment joining the points (2,-2) and (-14, 6) in the ratio 3 : 5 internally, lies in quadrant

(a) I

(b) II

(C) III

(d) IV

CONCEPT TO BE IMPLEMENTED

A. $\sf{The \: coordinate \: of \: the \: point \: where \: the \: line }$

$\sf{joining \: the \: points \: (x_1,y_1) \: and \: (x_2,y_2) \: in }$

$\sf{the \: ratio \: \: m :n \: \: is }$

$= \displaystyle \sf{ \bigg( \frac{mx_2+nx_1 \: }{m + n} \: \: , \: \frac{my_2+ny_1 \: }{m + n} \bigg) }$

B. We know that in two dimensional geometry the Cartesian plane is divided by coordinate axis in 4 quadrant

1. Quadrant I : Both the x - coordinates and y - coordinates are positive

2. Quadrant II : The x - coordinate is negative and the y - coordinate is positive

3. Quadrant III : Both the x - coordinates and y - coordinates are negative

4. Quadrant IV : The x - coordinate is positive and the y - coordinate is negative

EVALUATION

Here the given points are (2,-2) and (-14, 6)

The ratio is 3 : 5

The coordinates of the point which divides the line segment joining the points (2,-2) and (-14, 6) in the ratio 3 : 5 internally is

$\displaystyle \sf{ = \bigg( \frac{(3 \times - 14)+(5 \times 2) \: }{3 + 5} \: \: , \: \frac{(3 \times 6) + (5 \times - 2) \: }{3 + 5} \bigg) }$

$\displaystyle \sf{ = \bigg( \frac{ - 42 + 10}{8} \: \: , \: \frac{18 - 10 }{8} \bigg) }$

$\displaystyle \sf{ = \bigg( \frac{ - 32}{8} \: \: , \: \frac{8 }{8} \bigg) }$

$\displaystyle \sf{ = ( - 4 \: , 1) }$

The x - coordinate = - 4 which is negative

The y - coordinate = 1 which is positive

So the point lies on Quadrant II

FINAL ANSWER

Hence the correct option is (b) II

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ locate the following points on the cartesian plane(aEr) (0,a),(a,0),(-a, 0),(0,-a)

https://brainly.in/question/26822338

2. On a coordinate grid, the location of a bank is (–4, 8) and the location of a post office is (2, 0).

https://brainly.in/question/23287117