The point C (–1,2) divides the line segment AB in the ratio 3:4, whe

Question

The point C (–1,2) divides the line segment AB in the ratio 3:4, where the coordinates of A is (2, 5). The coordinates of B are___________.

Options:

A . (–5, –2)

B . (–1, – 2)

C . (–4, – 2)

D . (5, – 4)

Answer: Option A
:
A
If a point

P (x, y)

divides a line segment joining

(x_{1}, y_{1}) and (x_{2}, y_{2})

in the ratio

m : n

, then the coordinates of P are given by:

x = \frac{m x_{2} + n x_{1}}{m + n}, y = \frac{m y_{2} + n y_{1}}{m + n}

Let

C (- 1, 2)

dividethe line joining

A (2, 5)

and

B (x, y)

in the ratio 3:4.
Then,

C (\frac{3 x + 8}{7}, \frac{3 y + 20}{7})

= C(-1, 2)

\Rightarrow \frac{3 x + 8}{7} = - 1 3 x + 8 = - 7 \Rightarrow x = - 5 \Rightarrow \frac{3 y + 20}{7} = 2 3 y + 20 = 14 \Rightarrow y = - 2

Thus, thecoordinates of B are

B (- 5, - 2) .

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. The points (a,a),(–a,−a) and (–√3a,√3a) are the vertices of a/an _____ triangle....(a,a),(–a,−a) and (–√3a,√3a) are the vertices of a/an _____ triangle.

Question 2. Mid-point of the line-segment joining the points (– 5, 4) and (9, – 8) is: ....

Question 3. The co-ordinates of the points which divides the line joining (– 2, – 2) and (– 5, 7) in the r....5, 7) in the ratio 2 : 1 is _____.

Question 4. If the direction cosines of a variable line in two adjacent positions be l, m, n and l + a, m + b, n + c and the small a....small angle between the two positions be θ, then :

Question 5. Direction cosines of the line which is perpendicular to the lines whose direction ratios are 1, –1, 2 and 2, 1, &....–1, 2 and 2, 1, –1 are given by :

Question 6. The equation of the plane passing through the points (1,-3,-2) and perpendicular to planes x +2y+2z=5 and 3x+3y+2z=8, is....(1,-3,-2) and perpendicular to planes x +2y+2z=5 and 3x+3y+2z=8, is

Question 7. If (l1,m1,n1) and (l2,m2,n2,) are d.c.'s of ¯¯¯¯¯¯¯¯¯¯OA, ¯¯¯¯¯¯¯¯OB such that ∠AOB=θ where ‘O�....d.c.’s of the internal bisector of the angle ∠AOB are

Question 8. If the lines x−12=y+13=z−14 and x−31=y−k1=z1 intersect, then k =....

Question 9. The equation of the plane passing through the points (2, –4, 0), (3, –4, 5) and parallel to the line 2x = ....to the line 2x = 3y = 4z is :

Question 10. The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line (12)x=(13)....= 5 measured parallel to the line (12)x=(13)y=(−16)z is :

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers