Selina solutions concise maths class 9 icse Solutions for Chapter 26 chapter 26 co ordinate geometry

For each equation given below; name the dependent and independent variables.

(i) y = (?/ ?) ? − ?

(ii) x = 9y + 4

(iii) ? = (??+?)/ ?

(iv) ? = ?/ ? (?? + ?)

Plot the following points on the same graph paper:

(i) (8, 7)

(ii) (3, 6)

(iii) (0, 4)

(iv) (0, -4)

(v) (3, -2)

(vi) (-2, 5)

(vii) (-3, 0)

(viii) (5, 0)

(ix) (-4, -3)

Find the values of x and y if:

(i) (x – 1, y + 3) = (4, 4,)

(ii) (3x + 1, 2y – 7) = (9, – 9)

(iii) (5x – 3y, y – 3x) = (4, -4)

Use the graph given alongside, to find the coordinates of the point (s) satisfying the given condition:

(i) The abscissa is 2.

(ii) The ordinate is 0.

(iii) The ordinate is 3.

(iv) The ordinate is -4.

(v) The abscissa is 5.

(vi) The abscissa is equal to the ordinate.

(vii) The ordinate is half of the abscissa.

State, true or false:

(i) The ordinate of a point is its x-coordinate.

(ii) The origin is in the first quadrant.

(iii) The y-axis is the vertical number line.

(iv) Every point is located in one of the four quadrants.

(v) If the ordinate of a point is equal to its abscissa; the point lies either in the first

quadrant or in the second quadrant.

(vi) The origin (0, 0) lies on the x-axis.

(vii) The point (a, b) lies on the y-axis if b = 0.

In each of the following, find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation:

In each of the following, the co-ordinates of the three vertices of a rectangle ABCD are given. By plotting the given points; find, in each case, the co-ordinates of the fourth vertex:

(i) A (2, 0), B (8, 0) and C (8, 4).

(ii) A (4, 2), B (-2, 2) and D (4, -2).

(iii) A (-4, -6), C (6, 0) and D(-4, 0).

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

A (-2, 2), B (8, 2) and C (4, -4) are the vertices of a parallelogram ABCD. By plotting the given points on a graph paper; find the co-ordinates of the fourth vertex D.

Also, form the same graph, state the co-ordinates of the mid-points of the sides AB and CD

A (-2, 4), C(4, 10) and D(-2, 10) are the vertices of a square ABCD. Use the graphical method to find the coordinates of the fourth vertex B. Also, find:

(i) The coordinates of the mid-point of BC;

(ii) The coordinates of the mid-point of CD and

(iii) The coordinates of the point of intersection of the diagonals of the square ABCD.

By plotting the following points on the same graph paper. Check whether they are collinear or not:

(i) (3, 5), (1, 1) and (0, -1)

(ii) (-2, -1), (-1, -4) and (-4, 1)

Plot the point A (5, -7). From point A, draw AM perpendicular to the x-axis and AN perpendicular to the y-axis. Write the coordinates of points M and N.

In square ABCD; A = (3, 4), B = (-2, 4) and C = (-2, -1). By plotting these points on a graph paper, find the coordinates of vertex D. Also, find the area of the square.

In rectangle OABC; point O is the origin, OA = 10 units along the x-axis, and AB = 8 units. Find the coordinates of vertices A, B, and C.