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Coordinate Geometry

Secondary 3 practice

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Coordinate Geometry practice questions

Secondary 3 topics from the O-Level Mathematics 4052 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 points A(2,−4)A(2, -4) and B(−1,1)B(-1, 1) are given. A point RR lies on the xx-axis such that AR=BRAR = BR. Find the xx-coordinate of RR.
Show the worked solution
  • Let R=(k,0)R = (k, 0) since RR lies on the xx-axis.
  • AR2=(k−2)2+(0−(−4))2AR^2 = (k - 2)^2 + (0 - (-4))^2
  • =(k−2)2+16= (k - 2)^2 + 16
  • BR2=(k−(−1))2+(0−1)2BR^2 = (k - (-1))^2 + (0 - 1)^2
  • =(k−(−1))2+1= (k - (-1))^2 + 1
  • Since AR=BRAR = BR, set AR2=BR2square both sidesAR^2 = BR^2 \quad \scriptsize\textit{square both sides}
  • (k−2)2+16=(k−(−1))2+1(k - 2)^2 + 16 = (k - (-1))^2 + 1
  • k2−4k+4+16=k2+2k+1+1expandk^2 - 4k + 4 + 16 = k^2 + 2k + 1 + 1 \quad \scriptsize\textit{expand}

Answer: 33

Example 2

Points A(k, 5)A(k,\ 5) and B(0, 0)B(0,\ 0) lie on a line with gradient 11. Find kk.
Show the worked solution
  • Gradient formula: m=y2−y1x2−x1m = \dfrac{y_2 - y_1}{x_2 - x_1}
  • 1=0−(5)0−k1 = \dfrac{0 - (5)}{0 - k}
  • 1=−5−k1 = \dfrac{-5}{-k}
  • −k=−5cross multiply-k = -5 \quad \scriptsize\textit{cross multiply}
  • k=5k = 5

Answer: 55

Example 3

The line y=−4x+cy = -4x + c passes through the point (4, −11)(4,\, -11). The line crosses the yy-axis at the point PP. Find the yy-coordinate of PP.
Show the worked solution
  • Since (4, −11)(4,\, -11) lies on y=−4x+cy = -4x + c, substitute x=4x = 4, y=−11y = -11:
  • −11=−4(4)+c-11 = -4(4) + c
  • −11=−16+c-11 = -16 + c
  • c=−11−(−16)c = -11 - (-16)
  • =5= 5
  • The line crosses the yy-axis where x=0x = 0:
  • y=−4(0)+5y = -4(0) + 5
  • =5= 5

Answer: 55

Questions parents ask

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Which syllabus does this follow?

O-Level Mathematics (4052), 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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