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Geometry - Coordinates in all four quadrants

Grade 6IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Cartesian Plane: A grid formed by a horizontal line (x-axis) and a vertical line (y-axis) intersecting at the Origin (0,0).

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Ordered Pairs: Points are written as (x, y), where x is the horizontal position and y is the vertical position.

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Quadrants: The plane is divided into four sections: Quadrant I (+, +), Quadrant II (-, +), Quadrant III (-, -), and Quadrant IV (+, -).

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Plotting Points: Start at the origin, move left or right along the x-axis, then move up or down along the y-axis.

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Horizontal and Vertical Lines: Points on a horizontal line have the same y-coordinate; points on a vertical line have the same x-coordinate.

📐Formulae

Horizontal Distance=∣x2−x1∣ (when y-coordinates are the same)\text{Horizontal Distance} = |x_2 - x_1| \text{ (when y-coordinates are the same)}

Vertical Distance=∣y2−y1∣ (when x-coordinates are the same)\text{Vertical Distance} = |y_2 - y_1| \text{ (when x-coordinates are the same)}

Midpoint=(x1+x22,y1+y22)\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

💡Examples

Problem 1:

Identify which quadrant the point P(−4,−2)P(-4, -2) lies in.

Solution:

Quadrant III

Explanation:

In Quadrant III, both the x-coordinate and the y-coordinate are negative. Since -4 and -2 are both negative, the point is in the third quadrant.

Problem 2:

Find the distance between the points A(−3,5)A(-3, 5) and B(4,5)B(4, 5).

Solution:

7 units

Explanation:

Since the y-coordinates are the same (5), the points lie on a horizontal line. The distance is the absolute difference between the x-coordinates: ∣4−(−3)∣=∣4+3∣=7|4 - (-3)| = |4 + 3| = 7.

Problem 3:

Three vertices of a rectangle are (1,2)(1, 2), (5,2)(5, 2), and (5,−3)(5, -3). Find the coordinates of the fourth vertex.

Solution:

(1,−3)(1, -3)

Explanation:

In a rectangle, sides are parallel to the axes. The point (1,2)(1, 2) and (5,2)(5, 2) form the top side. The point (5,2)(5, 2) and (5,−3)(5, -3) form the right side. To complete the rectangle, the fourth point must share the x-coordinate of the first point (1) and the y-coordinate of the third point (-3).