Find the ratio in which the x-axis cuts the join of the points A(4, 5) and B(- 10, -2). Also, find the point of intersection.
Let the point which cuts the join of A(4, 5), and B(-10, -2) in the ratio k : 1 be P(x, 0)
Formula: If $k: 1$ is the ratio in which the join of two points is divided by another point $(x,$, y), then
$\mathrm{x}=\frac{\mathrm{kx}_{2}+\mathrm{x}_{1}}{\mathrm{k}+1}$
$\mathrm{y}=\frac{\mathrm{ky}_{2}+\mathrm{y}_{1}}{\mathrm{k}+1}$
Taking for the y co-ordinate,
$0=\frac{\mathrm{k} \times-2+5}{\mathrm{k}+1}$
$\Rightarrow 2 \mathrm{k}=5$
$\Rightarrow \mathrm{k}=\frac{5}{2}$
Therefore
$x=\frac{\frac{5}{2} \times-10+4}{\frac{5}{2}+1}$
$x=\frac{-50+8}{5+2}$
$x=\frac{-42}{7}$
$x=-6$
Therefore, the ratio in which $x$-axis cuts the join of the points $A(4,5)$ and $B(-10,-2)$ is 5 : 2and the point of intersection is $(-6,0)$.
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,