Cartesian Coordinate System

Q. Gloria is walking along the path joining (−2, 3) and (2, −2), while Suresh is walking along the path joining (0, 5) and (4, 0). Represent this situation graphically.

Q.

The $y$ coordinate is known as __

Q. The point (0, 2) lies in the 3rd quadrant.

1. True
2. False

Q.

The point P (a, b) is first reflected in the origin and then reflected in the y-axis to P'. If P' has co-ordinates (4, 6); evaluate a and b.

Q.

Question 167

In a five-digit number, digit at ten's place is 4, digit at unit's place is one - fourth of ten's place digit, digit at hundred's place is 0, digit at thousand's place is 5 times of the digit at unit's place and ten thousand's place digit is double the digit at ten's place. Write the number.

Q.

What is the area of a triangle whose vertices are (0, 4), (0, 0) and (3, 0)?

1. 6 square units

2. 8 square units

3. 12 square units

4. 10 square units

Q. Write the coordinates of a point on X-axis which is equidistant from the points (−3, 4) and (2, 5).

Q.

The point P (3, 4) is reflected to P' in the x-axis; and O' is the image of O (the origin) when reflected in the line PP'. Write :

(i) the co-ordinates of P' and O'.

(ii) the length of the segments PP' and OO',

(iii) the perimeter of the quadrilateral POP'O',

(iv) the geometrical name of the figure POP'O'.

Q. P is a point (a, b) in the first quadrant . If two circles which pass through P and touch both the coordinate axes cut at right angles, then

Q.

The point P (x, y) is first reflected in the x-axis and then reflected in teh origin to P'. If P' has co-ordinats (-8, 5); evaluate x and y.

Q.

A point P(-3, 2) is the midpoint of a line segment AB.If coordinates of B are (5, -2), find the coordinates of A.

1. (-11, 6)

2. (11, 6)

3. (11, -6)

4. (-11, -6)

Q. 43. A rectangle PQRS joins the points P, Q, R, S.Co-ordinates of P and R be (2, 3) and (8, 11) respectively. The line QS is known to be parallel to the y-axis. Then coordinates of Q and S are: (1). (0, 7) and (10, 7) (2). (5, 2) and (5, 12) (3). (7, 6) and (7, 10) (4). (7, 2) and (7, 12)

Q.

The x coordinate is known as __

Q.

The point P (5, 3) was reflected in the origin to get the image P'.

(a) Write down the co-ordinates of P'.

(b) If M is the foot of the perpendicular from P to the x-axis, find the co-ordinates of M.

(c) If N is the foot of the perpendicular from P' to the x-axis, find the co-ordinates of N.

(d) Name the figure PMP'N.

(e) Find the area of the figure PMP'N.

Q.

In the figure given, line APB meets the X axis at A, y-axis at B. P is a point (-4, 2) & AP : BP = 1 : 2 . Write down the coordinates of A and B.

1. A(-6, 0), B(0, 6)

2. A(-4, 0), B(0, 4)

3. A(-5, 0), B(0, 6)

4. A(-5, 0), B(0, 4)

5. A(-6, 0), B(0, 4)

6. A(-4, 0), B(0, 6)

Q. Which of the following statements is/are correct?

1. Abscissa is the distance of the point from the X-axis.
2. Ordinate is the distance of the point from the Y-axis.
3. A point on the X-axis is not a part of any quadrant.
4. The first coordinate in the representation of a point is the abscissa and the second coordinate is the ordinate.

Q. Two coordinates are enough to represent a point in 2 dimensional space.

1. True
2. False

Q.

A (1, 1), B (5, 1), C(4, 2) and D (2, 2) are vertices of a quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A', B', C' and D' respectively. Locate A', B', C' and D' on the graph sheet and write their co-ordinates. Are D, A, A' and D' collinear ?

Q. ABCD is a quadrilateral the p(3, 7) and q(7, 3) are coordinates of midpoints of diagonals AC and BD respectively then find the corrdinates of midpoint of pq.

Q. Median is given by the x-coordinate of the point of intersection of the more than type ogive and less than type ogive?

1. True
2. False

Q.

If the centre of a circle is (2a, a-7), then the values of 'a', if the circle passes through the point (11, -9) and has diameter $10\sqrt{2}$ units will be:

1. 5 and 3

2. 3 and 4

3. 4 and 5

4. 5 and 2

Q.

The points A(2, 3), B(4 , 5) & C(7, 2) are the vertices of ∆ ABC.

∆A”B”C” is the image of ∆ ABC, when reflected in – axis.

Mention the special name of quadrilateral BCC”B” & find its area.

1. Parallelogram, 14

2. Isosceles Trapezium, 12

3. Parallelogram, 21

4. Rectangle, 14

5. Isosceles Trapezium, 21

6. Rectangle, 12

Q. Find the coordinates of the point which divides the line segment joining (-3, 5) and (4, -9) internally in the ratio 1 : 6.

1. (-2, -3)
2. (2, 3)
3. (-2, 3)
4. (2, -3)

Q.

Given below are the coordinates of points in a plane. Find out abscissa and ordinate of the given points.

(2, 3), (4, 5), (7, 8), (11, 15)

1. Abscissa - 2, 5, 7, 11

   Ordinate - 3, 4, 8, 15

2. Abscissa - 3, 4, 7, 11

   Ordinate - 2, 5, 8, 15

3. Abscissa - 2, 4, 7, 11

   Ordinate - 3, 5, 8, 15

4. Abscissa - 2, 4, 15, 11

   Ordinate - 3, 5, 8, 7

Q.

Given P (–3, 2) and Q (4, 5), and the join of PQ is intersected by -axis at R. Find the coordinates of R.

1. m : n = 3 : 4

2. m : n = 5 : 8

3. m : n = 4 : 3

4. m : n = 9 : 2

Q.

Any point on the y-axis can be represented as $(0,y)$. State whether true or false.

1. False

2. True

Q. Question 6
Find the coordinates of the point Q on the X-axis which lies on the perpendicular bisector of the line segment joining the points A(-5, -2) and B(4, -2). Name the type of triangle formed by the point Q, A and B.

Q. If the two coordinate axes are not perpendicular, but inclined at an angle of 60 degrees, then the number of coordinates used to represent a point is

1. 1
2. 2
3. 3
4. 4

Q.

Coordinates of a point on the x-axis are ________

1. (x, 0)

2. (0, 0)

3. (0, x)

4. (0, y)

Q. The ratio in which the line joining the points $(3,4)$ and $(5,6)$ is divided by $x-$axis :

1. $2:3$ externally
2. $6:4$ externally
3. $3:2$ externally
4. none of these