Coordinate Geometry

Point (- 5, 0) corresponds to (x, y). Here, x-coordinate is - 5, i.e. negative and y-coordinate is 0. $\Rightarrow$So, the point (- 5, 0) lies on the negative x-axis.

(–5, –4) $\Rightarrow$ Both x and y coordinates are negative. When x < 0 and y < 0, the point lies in the third quadrant. So, the point (–5, –4) lies in the third quadrant. 

As the point $\biggl(- \frac{2}{3}, 0\biggr) \leftrightarrow (x,y) $ Here, x co-ordinate is $\frac{-2}{3}$, which is negative and y co-ordinate is 0. So, the point $\biggl(- \frac{2}{3}, 0\biggr)$lies on the negative x-axis.

The point is $\biggl(\frac{4}{5}, -2 \biggr)$. It corresponds to (x, y). When x > 0 and y < 0, the point lies in the 4^th quadrant. So, the point $\biggl( \frac{4}{5}, -2 \biggr)$ lies in the 4^th quadrant.

The point is (0, – 11) ^{_{$\leftrightarrow $}} (x, y) Here, x-coordinate is 0 and y-coordinate is – 11. So, the point lies on the negative y-axis.

The point (0, 3) ^{_{$\leftrightarrow $}} (x, y) Here, the x-coordinate is 0 and the y-coordinate is 3. $\therefore$ The point (0, 3) lies on the positive y-axis.

The point is (17, 9) $\leftrightarrow $ (x, y) Here, x > 0 and y > 0 and if x is positive and y is positive, then the point lies in the 1^st quadrant. So, point (17, 9) lies in the first quadrant.                                                 OR The sign of co-ordinate of a point is (+, +), which lies in 1^st quadrant. So, (17, 9) lies in the first quadrant.

As the point is (8, 0)         (8, 0) $\leftrightarrow $ (x, y) Here, x-coordinate is 8 which is greater than 0 and y-coordinate is 0, and when y-coordinate is 0, then the point lies on x–axis. As the x-coordinate is greater than 0, the point (8, 0) lies on positive x–axis.

The point is (11, – 15). Here, x-coordinate is 11 > 0 and y-coordinate is – 15 < 0, and the signs of the coordinates are (+, –), which lie in the 4^th quadrant. So, the point (11, – 15) lies in the 4^th quadrant.

When x-coordinate is 0, the point lies on the y–axis. $\therefore$ The point (0, 6) lies on the positive y–axis.

The point is (– 7, 6). Here, x co-ordinate is – 7 < 0 and y co-ordinate is 6 > 0 i.e. x < 0 and y > 0, and when x is negative and y is positive, then the point lies in 2^nd quadrant. So, the point (– 7, 6) lies in the 2^nd quadrant.

As the point is (7, 0),         (7, 0) $\leftrightarrow $ (x, y) Here, x co-ordinate is 7 which is positive and y co-ordinate is 0, and when y co-ordinate is 0, then the point lies on x–axis. So, the point (7, 0) lies on positive x–axis.

The point is $\biggl( \frac{-8}{6}, \frac{-7}{3} \biggr)$. Here, x-coordinate is $\frac{-8}{6}$, which is negative, and y-coordinate is $\frac{-7}{3}$, which is also negative. i.e. x < 0 and y < 0 When x < 0 and y < 0, the point lies in the third quadrant. So, the point $\biggl( \frac{-8}{6}, \frac{-7}{3} \biggr)$ lies in the third quadrant.

The point is (0, – 3). Here, y co-ordinate is – 3, which is negative and when x co-ordinate is zero, then the point lies on y-axis. So, the point (0, – 3) lies on the negative y-axis.

The point is (– 2, 5). Here, x-co-ordinate is – 2 < 0 and y co-ordinate is 5 > 0. And when x < 0 and y > 0 in the point (x, y), then the point lies in the second quadrant. So, the point (– 2, 5) lies in the 2^nd quadrant.                                                             OR The signs of the co-ordinates of point are (–, +), which lies in the 2^nd quadrant. So, the point (– 2, 5) lies in the 2^nd quadrant.