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Question
The distance between points P(–1, 1) and Q(5, –7) is ______
Options
11 cm
10 cm
5 cm
7 cm
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Solution
10 cm
Let P(x1, y1) = P( -1, 1) and Q(x2, y2) = Q(5, -7)
Here, x1 = -1, y1 = 1, x2 = 5, y2 = -7
By distance formula,
d(P, Q) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
∴ d(P, Q) = `sqrt([5 - (-1)]^2 + (-7- 1)^2)`
∴ d(P, Q) = `sqrt(36 + 64)`
∴ d(P, Q) = `sqrt(100)`
∴ d(P, Q) = 10 cm
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By distance formula,
PQ = `sqrt(square + (y_2 - y_1)^2`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(square + square)`
= `sqrt(125)`
= `5sqrt(5)`
