Download App

The Straight Lines — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines4 Marks
Question
Find the equation to the straight line which bisects the distance between the points (a, b), (a', b') and also bisects the distance between the points (-a, b) and (a', -b').
✓

Answer

The line that bisects the distance between the points A(a, b), B(a', b') and between C(-a, b), D(a', -b') means a line passing through the midpoint of AB and CDmid point of AB is $\Big(\frac{\text{a}+\text{a}'}{2},\frac{\text{b}+\text{b}'}{2}\Big)$
mid point of CD is $\Big(\frac{-\text{a}+\text{a}'}{2},\frac{\text{b}-\text{b}'}{2}\Big)$
Equation is $\text{y}-\text{y}_1=\text{m}(\text{x}-\text{x}_1)$
$\text{y}-\text{y}_1=\frac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}(\text{x}-\text{x}_1)$
$\text{y}-\Big(\frac{\text{b}+\text{b}'}{2}\Big)=\frac{\Big(\frac{\text{b}-\text{b}'}{2}\Big)-\Big(\frac{\text{b}+\text{b}'}{2}\Big)}{\Big(\frac{-\text{a}+\text{a}'}{2}-\frac{\text{a}+\text{a}'}{2}\Big)}\Big(\text{x}-\Big(\frac{\text{a}+\text{a}'}{2}\Big)\Big)$
$\text{y}-\Big(\frac{\text{b}-\text{b}'}{2}\Big)=\frac{\frac{\text{b}}{2}-\frac{\text{b}'}{2}-\frac{\text{b}}{2}-\frac{\text{b}'}{2}}{-\frac{\text{a}}{2}+\frac{\text{a}'}{2}-\frac{\text{a}}{2}-\frac{\text{a}'}{2}}\Big(\text{x}-\Big(\frac{\text{a}+\text{a}'}{2}\Big)\Big)$
$\text{y}-\Big(\frac{\text{b}+\text{b}'}{2}\Big)=\frac{+\text{b}'}{\text{a}}\Big(\text{x}-\Big(\frac{\text{a}+\text{a}'}{2}\Big)\Big) $
$2\text{ay}-2\text{b}'\text{x}=\text{ab}-\text{a}'\text{b}'$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 4 marks)" from The Straight Lines→The Straight Lines — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

How many triangles can be obtained by joining 12 points, five of which are collinear?
→
Determine the number of 5 card combination out of a deck of if there is one ace in each combination.
→
In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:
The number of people who read exactly one the newspapers.
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{2\sin\text{x}-\sin2\text{x}}{\text{x}^3}$
→
Prove that the perpendicular drawn from the point (4, 1) on the join of (2, -1) and (6, 5) divides it in the ratio 5:8.
→
Show that $\sin100^\circ-\sin10^\circ$ is positive.
→
Differentiate the following functions with respect to x:$\frac{\text{x}+\cos\text{x}}{\tan\text{x}}$
→
A die is thrown. Describe the following events:

  1. A: a number less than 7
  2. B: a number greater than 7
  3. C: a multiple of 3
  4. D: a number less than 4
  5. E: an even number greater than 4
  6. F: a number not less than 3

Also find ${A\cup B}$, ${A\cap B}$, ${B\cup C}$, ${E\cap F}$, ${D\cap E}$, A –C, D–E, ${E\cap F'}$, F'.

→
A rod of length 12cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3cm from the end in contact with the x-axis.
→
In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Find:
How may drink tea and coffee both.
→