MCQ
The point which lies on the perpendicular bisector of the line segment joining the points $A(-2, – 5)$ and $B(2, 5)$ is :
- ✓$(0, 0)$
- B$(0, 2)$
- C$(2, 0)$
- D$(-2, 0)$
✓
Answer
Correct option: A.
$(0, 0)$
We know that, the perpendicular bisector of the any line segment divides the jjpe segment into two equal parts
i.e., the perpendicular bisector of the line segment always passes through the mid $-$ point of the line segment.
Mid $-$ point of the line segment joining the points $A (-2, -5)$ and $S(2, 5)$
$=\Big(\frac{-2+2}{2},\frac{-5+5}{2}\Big)=(0,0)$
$\Big[$ Since, mid-point of any line segment which passes throught the points $\left(x_1, y_1\right)$ and $\left(x_2, y_2\right)\Big]$
$=\Big[(\frac{\text{x}_1+\text{x}_2}{2},\frac{\text{y}_1+\text{y}_2}{2}\Big)\Big]$
Hence $, (0, 0)$ is the required point lies on the perpendicular bisector of the lines segment.
i.e., the perpendicular bisector of the line segment always passes through the mid $-$ point of the line segment.
Mid $-$ point of the line segment joining the points $A (-2, -5)$ and $S(2, 5)$
$=\Big(\frac{-2+2}{2},\frac{-5+5}{2}\Big)=(0,0)$
$\Big[$ Since, mid-point of any line segment which passes throught the points $\left(x_1, y_1\right)$ and $\left(x_2, y_2\right)\Big]$
$=\Big[(\frac{\text{x}_1+\text{x}_2}{2},\frac{\text{y}_1+\text{y}_2}{2}\Big)\Big]$
Hence $, (0, 0)$ is the required point lies on the perpendicular bisector of the lines segment.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The equation $\left(x^2+1\right)^2-x^2=0$ has
→If $x=a, y=b$ is the solution of the systems of equations $x-y=2$ and $x+y=4$, then the values of $a$ and $b$ are, respectively
→What is the probability that a leap year has $52$ Mondays ?
→If the product of zeros of the polynomial $f(x) a x^3-6 x^2+11 x-6$ is 4 , then $a=$
→For the following distribution :
The lower limit of the modal class is :
→|
Class
|
$60-70$ | $70-80$ | $80-90$ | $90-100$ | $100-110$ |
|
Frequency
|
$13$ | $10$ | $15$ | $8$ | $11$ |
In the figure, the value of $x$ for which $DE \| AB$ is :
→If the $2^{\text {nd }}$ term of an A.P. is 13 and $5^{\text {th }}$ term is 25 , what is its $7^{\text {th }}$ term?
→The probability that a number selected at random from the numbers $\{1, 2, 3,..., 15\}$ is a multiple of $4,$ is :
→A tangent $PQ$ at point of contact $P$ to a circle of radius $12\ cm$ meets the line through centre $O$ to a point $Q$ such that $OQ = 20\ cm,$ length of tangent $PQ$ is :
→If the probability of occurrence of an event is p then the probability of non-happening of this event is: