Practice Formula (3.1) - Coordinate Geometry - IB 10 Mathematics – Group 5, Geometry & Trigonometry

Practice: Formula

Lesson 3.1Coordinate Geometry

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6 sample questions

Question 1.
Find the midpoint of the segment joining (2, 4) and (8, 10).
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Average the x-coordinates, then average the y-coordinates.
Question 2.
Find the midpoint of the segment joining (−4, 6) and (2, −2).
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Use brackets around negative numbers.
3Question 3.
Which is the midpoint of the segment joining (x₁, y₁) and (x₂, y₂)?
- ((x₁ + x₂)/2, (y₁ + y₂)/2)
- ((x₂ − x₁)/2, (y₂ − y₁)/2)
- (x₁ + x₂, y₁ + y₂)
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Add, then halve.
4Question 4.
What is the midpoint of A(2, 3) and B(6, 7)?
- (4, 5)
- (2, 2)
- (8, 10)
- (3, 4)
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Average each pair of coordinates.
Question 5.
Find the equation of the perpendicular bisector of the segment joining A(2, 3) and B(6, 7), and check that the point (0, 9) is equidistant from A and B.
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The bisector passes through the midpoint with gradient −1 divided by the gradient of AB.
Question 6.
A triangle has vertices A(1, 2), B(7, 4) and C(5, 8). P is the midpoint of AB and Q is the midpoint of AC. Show that PQ is parallel to BC and half its length.
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Compare gradients for parallel lines and use the distance formula for lengths.

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