In this chapter, we will be learning about coordinate geometry.
We will start by understanding how to find the divisor of a line segment using the related ratio.
Next, we will explore parallel lines and perpendicular lines and how to identify them on a Cartesian plane.
We will also learn how to calculate the areas of polygons using coordinate geometry. Lastly, we will study equations of loci and how to derive the formula for the divisor of a line segment on a Cartesian plane.
We will then apply this formula in different situations.
• Relate the position of a point that divides a line segment with the related ratio
• Derive the formula for divisor of a line segment on a Cartesian plane, and hence use the formula in various situations
• Solve problems involving divisor of a line segment
• Make and verify conjectures about gradient of: (i) parallel lines, (ii) perpendicular lines and hence, make generalisations
• Solve problems involving equations of parallel and perpendicular lines
• Derive the formula of area of triangles when the coordinates of each vertex are known
• Determine the area of triangles by using the formula
• Determine the area of quadrilaterals by using the formula
• Make generalisation about the formula of area of polygons when the coordinates of each vertex are known, and hence use the formula to determine the area of polygons
• Solve problems involving areas of polygons
• Represent graphically, the locus that satisfies these conditions: (i) the distance of a moving point from a fixed point is constant, (ii) the ratio of a moving point from two fixed points is constant, and hence determine the equation of the locus.
• Solve problems involving equations of loci
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