Advertisement Remove all ads

Find the Equations to the Straight Lines Which Go Through the Origin and Trisect the Portion of the Straight Line 3 X + Y = 12 Which is Intercepted Between the Axes of Coordinates. - Mathematics

Answer in Brief

Find the equations to the straight lines which go through the origin and trisect the portion of the straight line 3 x + y = 12 which is intercepted between the axes of coordinates.

Advertisement Remove all ads

Solution

Let the line 3x + y = 12 intersect the x-axis and the y-axis at A and B, respectively.
At x = 0
0 + y = 12

\[\Rightarrow\] y = 12

At y = 0
3x + 0 = 12

\[\Rightarrow\] x = 4 

\[\therefore A \equiv \left( 4, 0 \right) \text{and } B \equiv \left( 0, 12 \right)\]

Let

\[y = m_1 x \text { and } y = m_2 x\] be the lines that pass through the origin and trisect the line 3x + y = 12 at P and Q.
∴ AP = PQ = QB
Let us find the coordinates of P and Q.

\[P \equiv \left( \frac{2 \times 4 + 1 \times 0}{2 + 1}, \frac{2 \times 0 + 1 \times 12}{2 + 1} \right) \equiv \left( \frac{8}{3}, 4 \right)\]

\[Q \equiv \left( \frac{1 \times 4 + 2 \times 0}{2 + 1}, \frac{1 \times 0 + 2 \times 12}{2 + 1} \right) \equiv \left( \frac{4}{3}, 8 \right)\]

Clearly, P and Q lie on \[y = m_1 x \text { and } y = m_2 x\] ,respectively.

\[\therefore 4 = m_1 \times \frac{8}{3} \text { and }8 = m_2 \times \frac{4}{3}\]

\[ \Rightarrow m_1 = \frac{3}{2} \text { and} m_2 = 6\]

Hence, the required lines are

\[y = \frac{3}{2}x \Rightarrow 2y = 3x \text { and } y = 6x\]

Concept: Straight Lines - Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.5 | Q 14 | Page 35
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×