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Any point on the x – axis is of the form A. (x, y) B. (0, y) C. (x, 0) D. (x, x)

The correct answer is C. (x, 0) Solution Any point on the x-axis has its ordinate 0. So, any point on the x-axis is of the form (x, 0).... View Article

The equation x = 7, in two variables, can be written as A. 1. x + 1. y = 7 B. 1. x + 0. y = 7 C. 0. x + 1. y = 7 D. 0. x + 0. y = 7

The correct answer is B. 1. x + 0. y = 7 Solution The Coefficient of y in the given equation x =7 is 0. So, the equation can be expressed... View Article

The graph of the linear equation 2x + 3y = 6 cuts the y – axis at the point A. (2, 0) B. (0, 3) C. (3, 0) D. (0, 2)

The correct answer is D. (0, 2)Solution Let 2x + 3y = 6 cut the y-axis at P. T Therefore at P x-coordinate = 0. On substituting x =... View Article

Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form A. (-9/2 , m) B. (n, -9/2) C. (0, -9/2) D. ( – 9, 0)

The correct answer is A. (-9/2 , m) Solution Solving the above equation 2x + 0y + 9 = 0 we obtain, 2x = -9 x = -9/2 As the... View Article

If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is A. 4 B. 6 C. 5 D. 2

The correct answer is A. 4Solution We know that, (2, 0) = (x, y) Substituting values of x and y in the given equation, we get... View Article

The equation 2x + 5y = 7 has a unique solution, if x, y are: A. Natural numbers B. Positive real numbers C. Real numbers D. Rational numbers

The correct answer is A. Natural numbersSolution Consider, 2x + 5y = 7 x 1 y 1 A. (1, 1) is a solution of 2x + 5y = 7... View Article

The linear equation 2x – 5y = 7 has A. A unique solution B. Two solutions C. Infinitely many solutions D. No solution

The correct answer is C. Infinitely many solutionsSolution By expressing y in terms of x in the equation 2x – 5y = 7, we obtain, 2x... View Article

Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the third quadrant.

Solution Let us plot the graph as per the given details. Then the graph can be represented as follows From the graph, we observe that, The... View Article

Points A (5, 3), B (-2, 3) and D (5, -4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.

Given Points A (5, 3), B (–2, 3) and D (5, –4) are three vertices of a square ABCD Find out We have to determine the coordinates... View Article

In FigureLM is a line parallel to the y-axis at a distance of 3 units. (i) What are the coordinates of the points P, R and Q? (ii) What is the difference between the abscissa of the points L and M?

Solution: (i) The coordinates of the points are: P = (3,2) R = (3,0) Q = (3,-1) (ii)The cartesian coordinates are of the form (x, y). The... View Article

Without plotting the points indicate the quadrant in which they will lie, if (i) ordinate is 5 and abscissa is – 3 (ii) abscissa is – 5 and ordinate is – 3 (iii) abscissa is – 5 and ordinate is 3 (iv) ordinate is 5 and abscissa is 3

Solution: The cartesian coordinates are of the form (x, y). The ordered pairs in the two-dimensional plane are referred to as the abscissa and... View Article

Plot the following points and check whether they are collinear or not: (i) (1, 3), (- 1, – 1), (- 2, – 3) (ii) (1, 1), (2, – 3), (- 1, – 2) (iii) (0, 0), (2, 2), (5, 5)

(i) (1, 3), (– 1, – 1), (– 2, – 3) The points (1, 3), (– 1, – 1), (– 2, – 3) lie in a straight... View Article

Plot the points (x, y) given by the following table:

X 2 4 -3 -2 3 0 y 4 2 0 5 -3 0 Solution The given points when pointing on the cartesian plan is shown below... View Article

Plot the following points and write the name of the figure obtained by joining them in order: P(- 3, 2), Q (- 7, – 3), R (6, – 3), S (2, 2)

Solution: The figure obtained on joining the points P(– 3, 2), Q (– 7, – 3), R (6, – 3), S (2, 2) in the order is a... View Article

Write the coordinates of each of the points P, Q, R, S, T and O from the Figure

Solution: The coordinates of the points P, Q, R, S, T and O are as listed below P = (1, 1) Q = (-3, 0) R = (-2, -3) S = (2, 1) T = (4, -2) O = (0, 0)... View Article

Write whether the following statements are True or False? Justify your answer. (i) Point (3, 0) lies in the first quadrant. (ii) Points (1, -1) and (-1, 1) lie in the same quadrant. (iii) The coordinates of a point whose ordinate is – 1/2 and abscissa is 1 are – 1/2 , 1. (iv) A point lies on y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0). (v) (-1, 7) is a point in the II quadrant.

Solution (i) Point (3, 0) lies in the first quadrant. The given statement is False Explanation: The points having x-coordinate as ‘0′... View Article

If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has A. x – coordinate = – 5 B. y – coordinate = 5 only C. y – coordinate = – 5 only D. y – coordinate = 5 or -5

The correct answer is D. y – coordinate = 5 or –5 Solution The location of any point on a plane is expressed by a pair of... View Article

The points (-5, 2) and (2, – 5) lie in the A. same quadrant B. II and III quadrants, respectively C. II and IV quadrants, respectively D. IV and II quadrants, respectively

The correct answer is C. II and IV quadrants, respectively Solution The location of any point on a plane is expressed by a pair of values... View Article

If y coordinate of a point is zero, then this point always lies A. in I quadrant B. in II quadrant C. on x – axis D. on y – axis

The correct answer is C. on the x-axis Solution If the y-coordinate of a point, i.e., the ordinate is zero, then this point always lies on... View Article

Points (1, – 1), (2, – 2), (4, – 5), (- 3, – 4) A. lie in II quadrant B. lie in III quadrant C. lie in IV quadrant D. do not lie in the same quadrant

The correct answer is D. do not lie in the same quadrant Solution Signs of coordinates of points in different quadrants: I... View Article

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