If the point C (–1, 2) divides internally the line segment joining A (2, 5) an

Sail E0 Webinar

Question

If the point C (–1, 2) divides internally the line segment joining A (2, 5) and B in ratio 3 : 4, find the coordinates of B. [3 MARKS]

Options:

Answer: Option A
:

Formula: 1 Mark
Concept:1 Mark
Answer: 1 Mark
Let the coordinates of B be $(α, β)$ .
It is given that AC:BC = 3:4.

So, the coordinates of C are:
$C (x, y) = (\frac{m x_{2} + n x_{1}}{m + n}), (\frac{m y_{2} + n y_{1}}{m + n})$
$\Rightarrow C (- 1, 2) = \frac{3 α + 4 \times 2}{3 + 4}, \frac{3 β + 4 \times 5}{3 + 4}$
$\Rightarrow C (- 1, 2) = \frac{3 α + 8}{7}, \frac{3 β + 20}{7}$
$\Rightarrow \frac{3 α + 8}{7} = - 1 a n d \frac{3 β + 20}{7} = 2$
$\Rightarrow α = - 5 a n d β = - 2$
Thus, the coordinates of B are (-5, -2).

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If A (–2, –1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram. Find the values of a....parallelogram. Find the values of a and b. [3 MARKS]

Question 2. Prove that (4, – 1), (6, 0), (7, 2) and (5, 1) are the vertices of a rhombus. Is it a square? [3 MARKS] ....vertices of a rhombus. Is it a square? [3 MARKS]

Question 3. Find the lengths of the medians of a triangle ABC whose vertices are A(7, –3), B(5, 3) and C(3, –1). [4 MARKS]....

Question 4. If A (1,2), B (4, y), C (x,6) and D (3,5) are vertices of a parallelogram ABCD, find the values of x and y. [4 MARKS]....

Question 5. If the coordinates of the mid points of the sides of a triangle are (1, 1), (2, – 3) and (3, 4) Find its centro....– 3) and (3, 4) Find its centroid. [4 MARKS]

Question 6. For what value of k are the points A(k, 2 – 2k) ,B(–k + 1, 2k) and C(–4 – k, 6 – 2k....C(–4 – k, 6 – 2k) are collinear ? [4 MARKS]

Question 7. The two opposite vertices of a square are (–1, 2) and (3, 2). Find the co-ordinates of the other two vertices. [4 MARK....Find the co-ordinates of the other two vertices. [4 MARKS]

Question 8. Find the area of the quadrilateral ABCD whose vertices are respectively A (1, 1), B (7, –3) C (12, 2) and D (7,21). [4....(7, –3) C (12, 2) and D (7,21). [4 MARKS]

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

GPOE / GPA Combined 1 Free Mock Test SAIL JO E-0 2024

ICA Combined 1 Free Revision Test SAIL JO E-0

RDIC Review Test SAIL JO E-0

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

RSP Combined 1 Free Revision Test SAIL JO E-0