Exam Practice Worksheet

Coordinate Geometry • SPM Paper 1 & 2

SPM KSSM Diagnostic Drill

Form 4 Chapter 7: Coordinate Geometry (Geometri Koordinat)

Total Marks: 40 Marks • Time Allowed: 50 Minutes

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A Bahagian A: SPM Paper 1 Format [16 Marks]

Answer all questions
Soalan 1 [4 Marks]

Point $P(h, 4)$ divides the line segment connecting point $A(-3, 10)$ and point $B(5, -2)$ internally in the ratio $m : n$. Find:

(a) The ratio $m : n$. [2 marks]

(b) The value of $h$. [2 marks]

Soalan 2 [4 Marks]

The points $P(2, k)$, $Q(5, 7)$, and $R(8, 11)$ are collinear. Find the value of $k$ by using two different methods:

(a) The concept of gradient. [2 marks]

(b) The shoelace formula for area. [2 marks]

Soalan 3 (Paper 1 Sec B) [8 Marks]

A point $P(x, y)$ moves such that its distance from point $A(-1, 3)$ and point $B(5, 1)$ satisfies the condition $PA^2 + PB^2 = 36$.

(a) Show that the equation of the locus of $P$ is $x^2 + y^2 - 4x - 4y + 1 = 0$. [4 marks]

(b) Show that the locus is a circle, and find its center and radius. [3 marks]

(c) Determine whether the origin $O(0,0)$ lies inside, on, or outside the circle. [1 mark]

B Bahagian B: SPM Paper 2 Format & Real-World KBAT [24 Marks]

Answer all questions
Soalan 4 (Paper 2 Standard) [10 Marks]

In quadrilateral $ABCD$, point $A$ is $(1, 4)$, $B$ is $(7, 6)$, and $C$ is $(9, 2)$. The line $AD$ is perpendicular to line $AB$, and line $CD$ is parallel to line $AB$.

(a) Find the equation of the line $CD$. [2 marks]

(b) Find the equation of the line $AD$. [2 marks]

(c) Hence, determine the coordinates of point $D$. [2 marks]

(d) Calculate the area of the quadrilateral $ABCD$. [4 marks]

Soalan 5 (KBAT Drone Air Corridor Geofencing) [8 Marks]
An autonomous agricultural inspection drone flies at a constant altitude. A high-voltage transmission substation is located at $S(3, 4)$ with an electromagnetic interference exclusion safety zone defined by the locus circle $(x - 3)^2 + (y - 4)^2 = 9$. The drone's planned straight flight path passes through waypoint $A(0, 8)$ and waypoint $B(8, 2)$ (coordinates in kilometers).

(a) Find the Cartesian equation of the drone's flight path line $AB$. [2 marks]

(b) Calculate the shortest perpendicular distance from the transmission substation $S$ to the flight path $AB$. [3 marks]

(c) Determine whether the drone will breach the electromagnetic interference safety zone of the substation. Justify your answer with mathematical evidence. [3 marks]

Soalan 6 (Non-Routine Synthesis) [6 Marks]

A circular locus has the equation $x^2 + y^2 - 6x - 8y + 21 = 0$. Find the range of values of $c$ such that the straight line $y = x + c$ intersects the circular locus at two distinct points.