Tag: section and mid-point formula

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Questions Related to section and mid-point formula

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

STATEMENT - 1 : The coordinates of the point P(x, y) which divides the line segment joining the points A$(x _1,  y _1)$ and B$(x _2,  y _2)$ internally in the ration $m _1$  :  $m _2$ are $\left ( \dfrac{m _1 x _2 -m _2 x _1}{m _1 + m _2} ,  \dfrac{m _1 y _2 - m _2 y _1}{m _1 + m _2}\right )$


STATEMENT - 2 : The mid-point of the line segment joining the points P $(p _1 y _1)$ and Q$(x _2, y _2)$ is $\left ( \dfrac{x _1+x _2}{2} , \dfrac{y _1 + y _2}{2} \right )$

  1. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

  2. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1

  3. Statement - 1 is True, Statement - 2 is False

  4. Statement - 1 is False, Statement - 2 is True
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement -1 is false,

As the formula is not for the internally it is when point divides externally.
Statement -2 is true.

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

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

  1. $(9,-22)$

  2. <span>$(-1,2)$</span>

  3. <span>$(-1,-2)$</span>

  4. <span>$(9,22)$</span>
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let point P be (x,y)
$x=\cfrac { 5\times (-1)-4\times (-1) }{ 5-4 } \\ x=\cfrac { -5+4 }{ 1 } \\ x=-1\\ y=\cfrac { 5\times (2)-4\times (3) }{ 5-4 } \\ y=\cfrac { 10-12 }{ 1 } \\ y=-2\\ \therefore P=(-1,-2)$