Tag: mid-point of a line segment

Questions Related to mid-point of a line segment

The ratio in which the joining of (-3,2) and (5,6) is divided by the y-axis is

maths section and mid-point formula midpoint of line segment mid point formula mid-point of a line segment

  1. 3:5

  2. 2:5

  3. 1:3

  4. 2:3

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Correct Option: A
Explanation:

Let the ratio be k:1 Then
x-coordinate of P = 0

$\dfrac{k\times 5+1\times -3}{k+1}=0$
$k=\dfrac{3}{5}$

Consider points $A(-1,3), B(-1,2)$. Find point $P$ which divides $AB$ externally in $\dfrac{5}{4}$.

maths section and mid-point formula midpoint of line segment mid point formula mid-point of a line segment

  1. $(9,-22)$

  2. $(-1,2)$

  3. $(-1,-2)$

  4. $(9,22)$

Show answer
Correct Option: C
Explanation:
Let point P be (x,y)
$x=\cfrac { 5\times (-1)-4\times (-1) }{ 5-4 } \\ x=\cfrac { -5+4 }{ 1 } \\ x=-1\\ y=\cfrac { 5\times (2)-4\times (3) }{ 5-4 } \\ y=\cfrac { 10-12 }{ 1 } \\ y=-2\\ \therefore P=(-1,-2)$