Directed Distance and the Distance Formula

Directed Distance: A(3, 4) to B(9, 4)

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If A(3, 4) and B(9, 4) are two points with the same ordinate, find the directed distance AB (from A to B).

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Directed Distance: A(−8, 0) to B(6, 0)

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If A(−8, 0) and B(6, 0), find the directed distance AB (from A to B).

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Directed Distance: A(4, 2) to B(1, 2)

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If A(4, 2) and B(1, 2), find the directed distance AB (from A to B).

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Sign of a Horizontal Directed Distance

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For two points with the same ordinate, the directed distance AB = x2 − x1 is positive when:

A is above B

B is to the right of A

B is to the left of A

A and B coincide

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Directed Distance: C(1, −2) to D(1, −8)

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If C(1, −2) and D(1, −8) are two points with the same abscissa, find the directed distance CD (from C to D).

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Directed Distance: C(−2, −3) to D(−2, 4)

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If C(−2, −3) and D(−2, 4), find the directed distance CD (from C to D).

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Sign of a Vertical Directed Distance

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For two points with the same abscissa, the directed distance CD = y2 − y1 is positive when:

D is above C

D is below C

C and D coincide

D is to the right of C

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Deriving the Distance Formula

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Right triangle PRQ used to derive the distance formula

In deriving the distance formula, d is the length of the hypotenuse of right triangle PRQ. Which theorem gives d² = |Δx|² + |Δy|²?

Angle Sum theorem

Law of Sines

Law of Cosines

Pythagorean theorem

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Apply the Distance Formula

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Using the distance formula, find the distance between \(P(3, -4)\) and \(Q(-2, 1)\). Give your answer in simplified radical form.

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Distance on a Horizontal Line

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If P and Q lie on the same horizontal line (so \(y_2 = y_1\)), the distance formula simplifies to \(d =\)

x2 − x1

|y2 − y1|

√(x2 + x1)

|x2 − x1|

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Directed Distance: A(3, 4) to B(9, 4)

Correct Answer

Explanation

Directed Distance: A(−8, 0) to B(6, 0)

Correct Answer

Explanation

Directed Distance: A(4, 2) to B(1, 2)

Correct Answer

Explanation

Sign of a Horizontal Directed Distance

Correct Answer

Explanation

Directed Distance: C(1, −2) to D(1, −8)

Correct Answer

Explanation

Directed Distance: C(−2, −3) to D(−2, 4)

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Explanation

Sign of a Vertical Directed Distance

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Explanation

Deriving the Distance Formula

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Explanation

Apply the Distance Formula

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Explanation

Distance on a Horizontal Line

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Explanation

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