Bisection of Chords (AQA A-Level Mathematics): Quizzes

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Bisection of Chords
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What is a chord of a circle?

A line segment with both endpoints on circle

What is the midpoint MM of chord with endpoints A(x1,y1)A(x_1, y_1) and B(x2,y2)B(x_2, y_2)?

(x1+x22,y1+y22)\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

What is the perpendicular bisector of a chord?

Line perpendicular to chord through midpoint

Where does the perpendicular bisector of any chord pass through?

The centre of the circle

If a chord has slope 34\frac{3}{4}, what is the slope of its perpendicular bisector?

−43-\frac{4}{3}

How is the centre of a circle positioned relative to a chord's endpoints?

Equidistant from both endpoints

For chord with endpoints A(4,3)A(4, 3) and B(−4,−3)B(-4, -3), what is the midpoint?

(0,0)(0, 0)

What is the slope of chord ABAB with A(4,3)A(4, 3) and B(−4,−3)B(-4, -3)?

34\frac{3}{4}

For chord ABAB with slope −1-1, what is the perpendicular bisector's slope?

11

For chord with midpoint (3,3)(3, 3) and perpendicular bisector slope 11, what is its equation?

y=xy = x

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