Co-Ordinate Geometry

Third quadrant

Step 1: Recall the sign patterns for each quadrant. Step 2: Q1 has (+,+), Q2 has (-,+), Q3 has (-,-), Q4 has (+,-). Step 3: We need both x and y coordinates to be negative. Step 4: Only the third quadrant has the pattern (-,-), meaning both coordinates are negative.

X-axis

Step 1: Check the y-coordinate of point A(3, 0). Step 2: The y-coordinate is 0, which means the point is at zero distance from X-axis. Step 3: Points with y-coordinate = 0 lie on the X-axis. Step 4: Since x-coordinate is 3 ≠ 0, the point is not at origin, so it lies specifically on the positive X-axis.

5 units

Step 1: The x-coordinate represents the perpendicular distance from Y-axis. Step 2: For point P(-5, 0), the x-coordinate is -5. Step 3: Distance is always positive, so we take the absolute value. Step 4: Distance from Y-axis = |-5| = 5 units. The negative sign indicates direction (left of Y-axis), but distance is always positive.

(5, -2)

Step 1: Fourth quadrant has sign pattern (+,-), meaning x > 0 and y < 0. Step 2: Check each option: (2,3) has (+,+) - Q1, (-4,1) has (-,+) - Q2, (5,-2) has (+,-) - Q4, (-3,-6) has (-,-) - Q3. Step 3: Only (5,-2) matches the fourth quadrant pattern. Step 4: Therefore, (5,-2) lies in the fourth quadrant.