Coordinate geometry

The slope of the line 4x − 3y + 6 = 0 is 4/3.. Rewriting the line's equation in slope-intercept form, y = mx + c, yields y = (4/3)x + 2, which identifies the slope as 4/3.

The distance from the origin to (3, 4) is √(3²+4²)=5.. Using the Euclidean distance formula, the distance from the origin to the point is the square root of 3 squared plus 4 squared, which equals 5.

Using the Euclidean distance formula d=√[(x₂−x₁)²+(y₂−y₁)²] with (x₁,y₁)=(0,0) and (x₂,y₂)=(3,4) gives √(9+16)=√25=5. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Many students mistakenly add the coordinates (3+4) and think the distance is 7, overlooking the need to apply the Pythagorean theorem.
• !Students often incorrectly apply a negative sign when rearranging the equation, leading to an incorrect slope. This mistake can be avoided by carefully balancing the equation when isolating the y term.
• !People often get confused by not squaring the radius in the equation or forgetting the equation of a circle with centre at the origin.
• !Some students may confuse the eccentricity of a circle with that of a parabola or an ellipse.
• !Option D is incorrect because 7 is simply the arithmetic sum of the coordinates, which fails to account for the geometry of a right triangle.

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Run a focused 10-question mini-mock on Coordinate geometry and see it stick.