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Find distance between point A(–1, 1) and point B(5, –7): Solution: Suppose A(x_1, y_1) and B(x_2, y_2) x_1 = –1, y_1 = 1 and x_2 = 5, y_2 = –7 Using distance formula

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Question

Find distance between point A(–1, 1) and point B(5, –7):

Solution: Suppose A(x1, y1) and B(x2, y2)

x1 = –1, y1 = 1 and x2 = 5, y2 = –7

Using distance formula,

d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

∴ d(A, B) = `sqrt(square +[(-7) + square]^2`

∴ d(A, B) = `sqrt(square)`

∴ d(A, B) = `square`

Fill in the Blanks
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Solution

Suppose A(x1, y1) and B(x2, y2)

x1 = –1, y1 = 1 and x2 = 5, y2 = – 7

Using distance formula,

d(A, B) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

∴ d(A, B) = \[\sqrt{\boxed{[5 - (-1)]^2} + [(-7) + \boxed{-1}]^2}\]

∴ d(A, B) = `sqrt(6^2 + (-8)^2`

∴ d(A, B) = `sqrt(36 + 64)`

∴ d(A, B) = \[\sqrt{\boxed{100}}\]

∴ d(A, B) = \[\boxed{10 \phantom{.}\text{units}}\]

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Chapter 5: Co-ordinate Geometry - Exercise

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