In the given figure, line APB meets the $x$-axis at A and $y$-axis at B . P is the point $(-4,2)$ and $AP : PB =1: 2$. Write down coordinates of A and B.
View full solution →Question types
Section and Mid- Point Formula question types
35 questions across 4 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.
35
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Sample Questions
Section and Mid- Point Formula questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the points $A (6,1), B (8,2), C (9,4)$ and $D (p, 3)$ are the vertices of a parallelogram, taken in order, find the value of $p$.
View full solution →Find the ratio in which the $y$-axis divides the line segment joining the points $(5,-6)$ and $(-1,-4)$. Also, find the point of intersection.
View full solution →Find the coordinates of the points of trisection (i.e., points dividing into three equal parts) of the line segment joining the points $A (2,-2)$ and $B (-7,4)$
View full solution →In what ratio does the point $C \left(\frac{5}{5}, \frac{11}{5}\right)$ divide the line segment joining the points $A (3,5)$ and $B (-3,-2)$ ?
View full solution →The line segment joining the points $(3,-4)$, and $(1,2)$ is trisected at the points P and Q . If the coordinates of P and Q are $(p,-2)$ and $\left(\frac{5}{3}, q\right)$ respectively, find the values of $p$ and $q$.
View full solution →The line segment joining $P (-4,5)$ and $Q (3,2)$ intersects the $y$-axis at R . PM and QN are perpendiculars from P and Q on $x$-axis. Find:
(a) the ratio $PR : RQ$
(b) the coordinates of R
(c) the area of the quadrilateral PMNQ.
View full solution →(a) the ratio $PR : RQ$
(b) the coordinates of R
(c) the area of the quadrilateral PMNQ.
Find the lengths of the medians of a triangle whose vertices are $A (7,-3), B (5,3)$ and $C (3,-1)$.
View full solution →P and Q are the points on the line segment joining the points $A (3,-1)$ and $B (-6,5)$ such that $AP = PQ = QB$. Find the co-ordinates of P and Q .
View full solution →The base BC of an equilateral triangle ABC lies on $y$-axis. The coordinates of point C are $(0,-3)$. If the origin is the mid-point of the base BC , find the coordinates of the points A and B .
View full solution →If $A (1,3), B (-1,2), C (2,5)$ and $D (x, y)$ are the vertices of a parallelogram ABCD , then the value of $x$ is:
- A$3$
- B$4$
- C$0$
- D$\frac{3}{2}$
The vertices of a parallelogram in order are $A (1,2), B (4, y), C (x, 6), D (3,6)$. The value of $x$ and $y$ respectively are:
- A6, 2
- B3, 6
- C5, 6
- D1, 4
The point which lies on the perpendicular bisector of the line segment joining the points $A (-2,-5)$ and $B (2,5)$ is:
- A$(0,0)$
- B$(0,2)$
- C$(2,0)$
- D$(-2,0)$
If the coordinates of one end of a diameter of a circle are $(2,3)$ and the coordinates of its centre are $(-2,5)$, then the coordinates of the other end of the diameter are:
- A$(-6,7)$
- B$(6,-7)$
- C$(6,7)$
- D$(-6,-7)$
If the mid-point of the line segment joining the points $P (6, b-2)$ and $Q (-2,4)$ is $(2,-3)$, then the value of $b=$
- A-5
- B-6
- C-7
- D-8
Assertion (A) : If the points $A (p, 1), B (8,2), C (9,4)$ and $D (7,3)$ are the vertices of a parallelogram, taken in order, then the value of $p$ is 6 .
Reason (R) : Diagonals of a parallelogram bisect each other at right angles.
View full solution →Reason (R) : Diagonals of a parallelogram bisect each other at right angles.
Assertion (A) : Points $(1,7),(4,2),(-1,-1)$ and $(-4,0)$ are the vertices of a square.
Reason (R) : If all the sides of a quadrilateral are equal and the diagonals are also equal, then the quadrilateral is a square.
View full solution →Reason (R) : If all the sides of a quadrilateral are equal and the diagonals are also equal, then the quadrilateral is a square.
Assertion (A) : Coordinates of the mid-point of the line segment joining the points $(-4,5)$ and $(2,-1)$ are $(-1,2)$.
Reason (R) : The mid-point of a line segment divides it in the ratio $1: 1$.
View full solution →Reason (R) : The mid-point of a line segment divides it in the ratio $1: 1$.
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