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Coordinate Geometry

Secondary 3 Additional Math practice

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Coordinate Geometry practice questions

Secondary 3 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

The midpoint of A(−7, 3)A(-7,\, 3) and BB is M(−1, 0)M(-1,\, 0). Find the coordinates of BB.
Show the worked solution
  • If M is the midpoint of AB,\text{If } M \text{ is the midpoint of } AB,
  • −7+xB2=−1and3+yB2=0\frac{-7 + x_B}{2} = -1 \quad \text{and} \quad \frac{3 + y_B}{2} = 0
  • −7+xB=−2and3+yB=0-7 + x_B = -2 \quad \text{and} \quad 3 + y_B = 0
  • xB=−2+7andyB=0−3x_B = -2 + 7 \quad \text{and} \quad y_B = 0 - 3
  • xB=5andyB=−3x_B = 5 \quad \text{and} \quad y_B = -3
  • ∴B=(5, −3)\therefore B = (5,\, -3)

Answer: x=5,y=−3x=5,y=-3

Example 2

The gradient of line l1l_1 is −12-\frac{1}{2}. Find the gradient of a line perpendicular to l1l_1.
Show the worked solution
  • For perpendicular lines: m1×m2=−1\text{For perpendicular lines: } m_1 \times m_2 = -1
  • −12×m2=−1-\frac{1}{2} \times m_2 = -1
  • m2=−1÷(−12)m_2 = -1 \div (-\frac{1}{2})
  • =2= 2

Answer: 22

Example 3

Find the area of quadrilateral PQRSPQRS with vertices P(−5, 3)P(-5,\, 3), Q(5, 2)Q(5,\, 2), R(5, −6)R(5,\, -6), S(−5, −7)S(-5,\, -7).
Show the worked solution
  • Using the Shoelace formula for quadrilateral PQRS:\text{Using the Shoelace formula for quadrilateral } PQRS:
  • Area=12∣xP(yQ−yS)+xQ(yR−yP)+xR(yS−yQ)+xS(yP−yR)∣\text{Area} = \frac{1}{2} |x_P(y_Q - y_S) + x_Q(y_R - y_P) + x_R(y_S - y_Q) + x_S(y_P - y_R)|
  • =12∣−5(9)+5(−9)+5(−9)−5(9)∣= \frac{1}{2} |-5(9) + 5(-9) + 5(-9) - 5(9)|
  • =12∣−45−45−45−45∣= \frac{1}{2} |-45 - 45 - 45 - 45|
  • =12×180= \frac{1}{2} \times 180
  • =90 square units= 90 \text{ square units}

Answer: 9090

Questions parents ask

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Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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