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SingaporeAdditional MathematicsQuick questions

Coordinate Geometry and Circles

Quick questions on Gradients and equations of straight lines: N(A)-Level Additional Mathematics

8short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is gradient?
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The gradient of the line through (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) measures how steep it is, as the change in yy divided by the change in xx:
What is length of a segment?
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The length (distance) between the two points comes from Pythagoras:
What is midpoint?
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The midpoint is the average of the two coordinates:
What is the equation of a line?
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To find the line through two points, first compute the gradient, then substitute one point into the point-gradient form, and finally rearrange into the form requested.
What are sign slips with negative coordinates?
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x−(−1)x - (-1) is x+1x + 1. Bracket negative coordinates before simplifying.
What is q1?
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Find the gradient of the line through (2,1)(2, 1) and (6,9)(6, 9). [2 marks]
What is q2?
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Find the midpoint of the segment joining (−2,5)(-2, 5) and (4,1)(4, 1). [2 marks]
What is q3?
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Find the equation of the line with gradient −3-3 passing through (1,2)(1, 2), in the form y=mx+cy = mx + c. [2 marks]

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