**Coordinate Geometry**

**Question 1In which quadrant or on which axis do each of the points (-2, 4),(3, -1), (-1, 0),(1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane.**

**Solution:**

The point (-2, 4) is having negative abscissa and positive ordinate.

∴ (-2,4) lies in the 2^{nd} quadrant.

The point (3, -1) is having positive abscissa and negative ordinate.

∴ (3, -1) lies in the 4^{th} quadrant.

The point (-1, 0) is having negative abscissa and zero ordinate.

∴ The point (-1, 0) lies on the negative x-axis.

The point (1, 2) is having the abscissa as well as ordinate positive.

∴ Point (1,2) lies in the 1^{st} quadrant.

The point (-3, -5) is having the abscissa as well as ordinate negative.

∴ Point (-3, -5) lies in the 3rd quadrant.

These points are plotted in the Cartesian plane as shown in the following figure as A(-2, 4); B(3, -1); C(-l, 0); D(l, 2) and E (-3, -5).

**Question 2Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.**

**Solution:**The given points are (-2, 8), (-1, 7), (0, -1.25), (1,3) and (3, -1).

To plot these points:

**(i)** We draw X’OX and YOY’ as axes.

**(ii)** We choose suitable units of distance on the axes.

**(iii)** To plot (-2,8), we start from O, take (-2) units on x-axis and then (+8) units on y – axis. We mark the point as A (-2, 8).

**(iv) **To plot (-1,7), we start from O, take (-1) units on x-axis and then (+7) units on the y – axis. We mark the point as B(-1, 7).

**(v)** To plot (0, -1.25), we move along 1.25 units below the x-axis on the y – axis and mark the point as C(0, -1.25).

**(vi)** To plot (1, 3), we take (+1) unit on the x-axis and then (+3) units on the y – axis. We mark the point as D(1, 3).

**(vii)** To plot (3, -1), we take (+3) units on the x-axis and then (-1) unit on the y – axis. We mark the point E(3, -1).