In what ratio is the line segment joining the points A(-4, 2) and B(8, 3) divided by the y-axis? Also, find the point of intersection.
Let the point which cuts the join of A(-4, 2) and B(8, 3) in the ratio k : 1 be P(0, y)
Formula: If $\mathrm{k}: 1$ is the ratio in which the join of two points are 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 x co-ordinate,
$0=\frac{\mathrm{k} \times 8+(-4)}{\mathrm{k}+1}$
$\Rightarrow 8 \mathrm{k}=4$
$\Rightarrow \mathrm{k}=\frac{1}{2}$
Therefore,
$y=\frac{\frac{1}{2} \times 3+2}{\frac{1}{2}+1}$
$y=\frac{3+4}{1+2}$
$y=\frac{7}{3}$
Therefore, the ratio in which the line segment joining the points A(-4, 2) and B(8, 3)
divided by the y-axis is 1 : 2 and the point of intersection is $\left(0, \frac{7}{3}\right)$
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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,