AC9M9A03Year 9AlgebraPractised on site

AC9M9A03 — Year 9 Algebra

Official Curriculum Content Description:

find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane

Worked Examples (1)

Example 1Midpoint & Length of Line Segments
Find the length of the line segment joining A(3,−4)A(3, -4) and B(8,−14)B(8, -14). Give your answer to 1 decimal place.
Common mistake: Adding coordinate values instead of finding their difference
Correct Answer:11.2 units11.2\text{ units}
Accepted: A unit is optional (units accepted).
Worked Solution:
Use Pythagoras's theorem d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}: d=(8−(3))2+(−14−(−4))2d = \sqrt{(8 - (3))^2 + (-14 - (-4))^2} d=(5)2+(−10)2=125≈11.2 unitsd = \sqrt{(5)^2 + (-10)^2} = \sqrt{125} \approx 11.2\text{ units}.

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