Coordinates of Points and Distances

Q.

Definition of x axis and y axis and origin

Q.

The abscissa or x-coordinate of any point on Y- axis is:

1. Three

2. One

3. Zero

4. Two

Q.

Coordinates of the vertices of a quadrilateral are $\left(2,-1\right),\left(0,2\right),\left(2,3\right)$ and $\left(4,0\right)$. The angle between its diagonals will be

1. $90°$

2. $0°$

3. ${\tan }^{-1}\left(2\right)$

4. ${\tan }^{-1}\left(\frac{1}{2}\right)$

Q.

C is the mid-point of PQ if P is (4, x), C is (y, -1) and Q is (-2, 4), then x and y respectively are

1. - 6 and 1

2. -6 and 2

3. 6 and -2

4. 6 and -1

Q.

The area of the triangle formed by the points P (0, 1), Q(0, 5) and R(3, 4) is

1. 16 sq.units

2. 8 sq.units

3. 4 sq.units

4. 6 sq.units

Q.

The distance of a point (2, 3) from the y - axis is.

1. 3 units

2. 2 units

3. 1 unit

4. 5 units

Q.

The distance of a point $(2,3)$ from the $x-$ axis is

1. $3$ units

2. $2$ units

3. $5$ units

4. $1$ unit

Q.

Consider the following two statements.

Statement -1 : The coordinate of a point on the x-axis is of the form $(x,0)$ and that of the point on the y-axis is $(0,y)$.

Statement -2 : The point of interaction of the axes is called the origin.

1. Statement 1 is true and Statement 2 is false.

2. Statement 1 is false and Statement 2 is true.

3. Both the statement 1 and 2 are true

4. Both the statement 1 and 2 are false

Q. The coordinates of point $C$ on negative x-axis are given as $(4q+16,7q-21)$.
Find the coordinates of $C$.

Q.

Find the coordinates of points of trisection of the line segment joining the points

A(-2, 8) and B(4, 12)

1. $\begin{array}{c}(9,\frac{4}{3})\\ (4,\frac{9}{5})\end{array}$

2. $\begin{array}{c}(0,\frac{28}{3})\\ (2,\frac{32}{3})\end{array}$

3. $\begin{array}{c}(4,\frac{5}{3})\\ (9,\frac{2}{3})\end{array}$

4. $\begin{array}{c}(8,\frac{5}{3})\\ (4,\frac{5}{9})\end{array}$

Q.

The distance of a point (2, 3) from the x- axis is

1. 5 units

2. 3 units

3. 2 units

4. 1 unit

Q.

Three boys, Ankur, Syed and David are sitting at equal distances on the boundary of a circular park of radius $20m.$ Each of them has a toy telephone to talk to each other. Find the length of the string that connects the telephones of any two of the boys.

1. 20√3

2. 40√3

3. 30√3

4. 10√3

Q. Plot the points A(4, 4) and B(-4, 4), join the lines OA, OB and BA. What figure do you obtain?

Q.

Find the coordinates of the points A and B from the following graph.

Q. Question 7
Any point on the x-axis is of the form:


A) (x, y)
B) (0, y)
C) (x, 0)
D) (x, -y)

Q. If a vertex of a triangle be $(1,1)$ and the middle points of the sides through it be $(-2,3)$ and $(5,2)$, find the other vertices.

Q. If abscissa is one third of the ordinate of a point $P(x,6)$ then find the value of $x$.

Q.

If (7, 3), (6, 1), (8, 2) and (p, q) are the vertices of a parallelogram, taken in order, then find the values of p and q.
p = ___ and q = ___

1. $p=9,q=4$

2. $p=9,q=6$

3. $p=5,q=6$

4. $p=4,q=9$

Q. The co - ordinate of base (BC ) of the isosceles triangle ABC are given by B(1 , 3) and C (-2 , 7 ) . Which of the following points can be the possible co - orientat of the vertex A

1. $[-7,\frac{1}{8}]$
2. (1 , 6 )
3. $[-\frac{1}{2},5]$
4. $[\frac{5}{6},6]$

Q. Find the co-ordinates of points whose. Whose abscissa is $-1\frac{2}{3}$ and ordinate is $-2\frac{1}{4}$

Q. If P - Q - R and d(Q, R) = 12 units, d(P, R) = 30 units, then d(P, Q) = ________ units.

1. 18

Q. Find the coordinates of a point where the line $x-\frac{1}{3}y=7$ intersects the co-ordinate axes.

Q. Solve :
(a) (i) Complete the table of values for $y=-x^2+5x$.

$x$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$y$	$-6$		$4$			$4$	$0$

(ii) On the grid, draw the graph of $y=-x^2+5x$ for $-1<x<6$.
(b) Write down the co-ordinates of the highest point on the graph.
(c) Use your graph to solve the equation $-x^2+5x=-3$.
(d) (i) On the grid draw, the line of symmetry for the graph.
(ii) Write down the equation of the line of symmetry for the graph.

Q. If AB = 20 units and M is the midpoint of AB, then AM = ________ units.

1. 10

Q. A point lies on the x- axis at a distance of $7$ units from the y - axis. What are its coordinates ? What will be the coordinates if it lies on y -axis at a distance of $-7$ units from x - axis ?

Q. In the given graph the letter that indicates the point $(0,3)$ is

1. P
2. S
   
3. R
4. None of these
   

Q.

Plot the Points (3, 5) and (-1, 3) on a graph paper and verify that the straight line passing through the points, also passes through the point (1, 4).

Q. $B(10,4),C(0,4)$ and $D(0,-2)$.

Q. What is the distance between point D and point H?

1. 5
2. 6
3. 4
4. 3

Q. If AB = 20 units and M is the midpoint of AB, then AM = ________ units.

1. 30
2. 20
3. 50
4. 10