Question

What is the distance between the points (–4, –8) and (10, –8)?

Answer 1

Given

• Two points (-4,-8) and (10,-8).

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To find

• Distance between the two given points.

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Solution

• Let the given points be A(-4,-8) and B(10,-8).

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Now, we have to find the distance between A and B.

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Using the distance formula

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$\: \: \: \: \: \: \: \: \star\bf\: \: \: {AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}$

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We have,

• $\sf{x_1 = -4\: and\: x_2 = 10}$
• $\sf{y_1 = -8\: and\: y_2 = -8}$

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Finding the distance

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$\rm:\implies\: \: \: \: \: \: \: \: {AB = \sqrt{(10 + 4)^2 + (-8 + 8)^2}}$

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$\rm:\implies\: \: \: \: \: \: \: \: {AB = \sqrt{(14)^2 + (0)^2}}$

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$\rm:\implies\: \: \: \: \: \: \: \: {AB = \sqrt{196 + 0}}$

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$\rm:\implies\: \: \: \: \: \: \: \: {AB = \sqrt{196}}$

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$\bf:\implies\: \: \: \: \: \: \: \: {AB = 14}$

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Hence,

• The distance between the given two points is 14 units.

Answer 2

Given that,

• There are two points (-4 , -8) and (10, -8)

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Let,

• A(-4 , -8)
• B(10 , -8)

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Formula for finding distance between two points,

$\boxed{\boxed{\bold\purple{\bigstar \: ab = \sqrt{(x2 - x1 )^{2} + (y2 - y1) {}^{2} } }}}$

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Here,

• x1 = -4
• x2 = 10
• y1 = -8
• y2 = -8

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Put the values in the formula,

Now,

$\rm:\implies \: AB = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} }$

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$\rm:\implies \: AB = \sqrt{(10 -( - 4)) {}^{2} + ( - 8 - ( - 8) ) {}^{2} }$

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$\rm:\implies \: AB = \sqrt{(10 + 4) {}^{2} + ( - 8 + 8) {}^{2} }$

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$\rm:\implies \: AB = \sqrt{(14) {}^{2} + (0) {}^{2} }$

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$\rm:\implies \: AB = \sqrt{(14) {}^{2} }$

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$\rm:\implies \: AB = \sqrt{14 \times 14}$

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$\rm:\implies \: \boxed{\boxed{\bold\purple{AB = 14units}}}\bigstar$

Hence, the distance between two points A and B is 14 units.