$A (1,2) B (2,3) C (3,4)$ are given points. Out of the following which is true ?
- A$AC + BC = AB$
- ✓$AB + BC = AC$
- C$C$ is a midpoint of $\overline{ AB }$.
- DA, B, C are not collinear
Answer: B.
View full solution →Question types
Coordinate Geometry question types
132 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
132
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
50 Q→02Fill In The Blanks[1 Marks ]
24 Q→03True False[1 Marks ]
8 Q→041 Marks Question
9 Q→052 Marks Questions
16 Q→063 Marks Question
11 Q→07Match The Following.
10 Q→084 Marks Questions
4 Q→Sample Questions
Coordinate Geometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the coordinates of the midpoint $P$ of the line segment joining $X$ and $Y$ is $(-2,3)$ then which is true ?
Note :The coordinates of the midpoint $=\left(\frac{x_1+x_2}{2^1} \frac{y_1+y_2}{2}\right)$
Note :The coordinates of the midpoint $=\left(\frac{x_1+x_2}{2^1} \frac{y_1+y_2}{2}\right)$
- A$X (-4,3), Y (2,2)$
- B$X (0,2), Y (-2,2)$
- ✓$X (-6,2), Y (2,4)$
- D$X (-4,-2), Y (0,4)$
Answer: C.
View full solution →For $\square$ $ABCD$, which group is true ?
| 1 | $\square$ $ABCD$ is a rhombus | (a) | $AC$ and $BD$ bisect |
| 2 | $\square$ $ABCD$ is a parallelogram | (b) | $AC$ and $BD$ bisect at right angle. |
| 3 | $\square$ $ABCD$ is a rectangle | (c) | $AC$ and $BD$ are congruent and bisect at right angle. |
| 4 | $\square$ $ABCD$ is a square | (d) | $AC$ and $BD$ are congruent and bisect at right angle. |
- A$(1 – c), (2 – d) (3 – a) (4 - b)$
- ✓$(1 – b), (2 – a) (3 – d) (4 - c)$
- C$(1 – b), (2 – c) (3 – d) (4 - a)$
- D$(1 – d), (2 – a) (3 – b) (4 - c)$
Answer: B.
View full solution →Distance is _______ of point $(x, y)$ to origin.
- ✓$\sqrt{x^2+y^2}$
- B$\sqrt{x^2-y^2}$
- C$x^2+y^2$
- D$x^2-y^2$
Answer: A.
View full solution →Perpendicular distance from $X$ - axis point $(-5,7)$ is _______
- A$-5$
- B$5$
- C$-7$
- ✓$7$
Answer: D.
View full solution →The perimeter of the triangle with vertices $(0,4)(0,0)$ and $(3,0)$ is _____________ units. (8, 12, 15)
View full solution →The point which divides the line segment joining the points $A(4,-1)$ and $B(-2,-3)$ in the ratio $1: 2$ lies in ____________ quadrant. (First, Third, Fourth)
View full solution →The distance between the points $(-5,8)$ and $(-2,-6)$ is $\ldots \ldots \ldots . . \sqrt{205}, \sqrt{502}, \sqrt{42}$
View full solution →The centroid of the triangle with vertices $(3,2)(7,5)$ and $(2,1)$ is ...... . $\left(\left(2, \frac{8}{3}\right),\left(3, \frac{8}{3}\right),\left(4, \frac{8}{3}\right)\right)$
View full solution →The area of the triangle whose vertices are $(4,0),(7,0)$ and $(8,0)$ is ......... sq. units. $(0,16,49)$
View full solution →The circumcenter of a right angle triangle is the midpoint of the hypotenuse.
The coordinates of the origin is $(0,0)$
View full solution →The midpoint of the line segment joining $A(8,-3), B(-3,5)$ is $(5,4)$.
View full solution →The point $P (-4,2)$ lies on the line segment joining $A (-4,6)$ and $B (-4,-6)$.
View full solution →The distance between the points $(2,3)$ and $(4,1)$ is $2 \sqrt{2}$.
View full solution →Find the ratio in which the line segment joining the points $(-3, 10)$ and $(6, -8)$ is divided by $(-1, 6)$.
View full solution →Find the area of the rhombus if its vertices are $(3, 0), (4, 5), (-1, 4)$ and $(-2, -1)$ taken in order.
[Hint: Area of a rhombus $=\frac{1}{2}$ (product of its diagonals)]
View full solution →[Hint: Area of a rhombus $=\frac{1}{2}$ (product of its diagonals)]
Find the coordinates of the point which divides the join of $(-1, 7)$ and $(4, -3)$ in the ratio $2 : 3.$
View full solution →Find the distance between the pair of points $(a, b), (-a, -b)$
View full solution →Find the distance between the pair of points $(-5, 7), (-1, 3)$
View full solution →If $A$ and $B$ are $(-2, -2)$ and $(2, -4)$ respectively, find the coordinates of $P$ such that $AP$ = $\frac{3}{7}$ $AB$ and $P$ lies on the line segment $AB$.
View full solution →Find the coordinates of a point $A$, where $AB$ is the diameter of a circle whose centre is $(2, -3)$ and $B$ is $(1, 4)$.
View full solution →If $(1, 2), (4, y), (x, 6)$ and $(3, 5)$ are the vertices of a parallelogram taken in order, find $x$ and $y$.
View full solution →Find the ratio in which the segment joining $A(1, -5)$ and $B(-4, 5)$ is divided by the $x$-axis. Also find the coordinates of the point of division.
View full solution →If $Q(0, 1)$ is equidistant from $P(5, -3)$ and $R(x, 6)$, find the values of $x$. Also find the distances $QR$ and $PR$.
View full solution →Find the point on the $x-$axis which is equidistant from $(2, -5)$ and $(-2, 9).$
View full solution →Name the type of quadrilateral formed, if any, by the points $(4, 5), (7, 6), (4, 3), (1, 2),$ and give a reason for your answer.
View full solution →Name the type of quadrilateral formed, if any, by the points $(-3, 5), (3, 1), (0, 3), (-1, -4),$ and give a reason for your answer.
View full solution →Name the type of quadrilateral formed, if any, by the points $(-1, -2), (1, 0), (-1, 2), (-3, 0),$ and give a reason for your answer.
View full solution →Find the distance between the points $(0, 0)$ and $(36, 15).$ Can you now find the distance between the two towns $A$ and $B$ discussed in Section $7.2.$
View full solution →| $A$ | $B$ |
| $Q.1. \square ABCD$ is a rhombus then its diagonals $AC$ and $BD.$ | $(a) X-$axis |
| $Q.2.$ What is the graph of $y = 0 ?$ | $(b)$ bisect at right angle |
| $(c) Y-$axis |
| $A$ | $B$ |
| $Q.1. \square ABCD$ is a rectangle then its diagonals $AC$ and $BD$ | $(a)$ bisect each other |
| $Q.2. \square ABCD$ is a parallelogram then its diagonals $AC$ and $BD ...........$ | $(b)$ are congruent and bisect |
| $(c)$ bisect at right angle |
| $A$ | $B$ |
| $Q.1.$ Distance between the points $(2, 3)$ and $(4, 1)$ is $..........$ | $(a) 4 \sqrt{2}$ |
| $Q.2. \square ABCD$ is a square then its diagonals $AC$ and $BD$ are $...........$ | $(b)$ congruent and bisect at right angle |
| $(c) 2 \sqrt{2}$ |
| $A$ | $B$ |
| $Q.1.$ Distance between the point $(2, 3)$ and $(5, 2)$ is $..........$ | $(a)$ Trisection point |
| $Q.2.$ The circumcenter of a right angle triangle is $.......$ of the hypotenuse. | $(b) \sqrt{10}$ |
| $(c)$ Mid point |
| $A$ | $B$ |
| $Q.1,$ What is the distance of $P(a, b)$ from the origin $?$ | $(a)\sqrt{a^2+b^2}$ |
| $Q.2.$ State the distance formula to find distance between the two points in a plane. | $(b) AB ^2=\left(x_1-y_1\right)^2+\left(x_2-y_2\right)^2$ |
| $(c) AB ^2=\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2$ |
Find the coordinates of the points which divide the line segment joining $A(-2, 2)$ and $B(2, 8)$ into four equal parts.
View full solution →To conduct Sports Day activities, in your rectangular-shaped school ground $ABCD,$ lines have been drawn with chalk powder at a distance of $1m$ each. $100$ flower pots have been placed at a distance of $1m$ from each other along $AD,$ as shown in Figure. Niharika runs $\frac{1}{4}$th the distance $AD$ on the $2nd$ line and posts a green flag. Preet runs $\frac{1}{5}$th the distance $AD$ on the eighth line and posts a red flag. What is the distance between both the flags$?$ If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag$?$
View full solution →Find the coordinates of the points of trisection of the line segment joining $(4, –1)$ and $(–2, –3)$.
View full solution →In a classroom, $4$ friends are seated at the four points $A, B, C$ and $D$ as shown in Fig. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, Don’t you think $ABCD$ is a square$?$ Chameli disagrees. Using distance formula, find which of them is correct.
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