How do you find the value of a given the points (1,1), (a,1) with a distance of 4?

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How do you find the value of a given the points (1,1), (a,1) with a distance of 4?

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Answer 1 · 2017-03-14T14:13:50

See the entire solution process below:

Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$ $d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)$

Substituting the values from the problem gives and solving for $a$ $a$ gives:

$4 = \sqrt{{(a - 1)}^{2} + {(1 - 1)}^{2}}$ $4 = sqrt((color(red)(a) - color(blue)(1))^2 + (color(red)(1) - color(blue)(1))^2)$

$4 = \sqrt{{(a - 1)}^{2} + 0^{2}}$ $4 = sqrt((color(red)(a) - color(blue)(1))^2 + 0^2)$

$4 = \sqrt{{(a - 1)}^{2} + 0}$ $4 = sqrt((color(red)(a) - color(blue)(1))^2 + 0)$

$4 = \sqrt{{(a - 1)}^{2}}$ $4 = sqrt((color(red)(a) - color(blue)(1))^2$

$4 = a - 1$ $4 = color(red)(a) - color(blue)(1)$ and $4 = - (a - 1)$ $4 = -(color(red)(a) - color(blue)(1))$ (Note: The square root of a term always produces a negative and positive result)

Solution 1)

$4 = a - 1$ $4 = a - 1$

$4 + 1 = a - 1 + 1$ $4 + color(red)(1) = a - 1 + color(red)(1)$

$5 = a - 0$ $5 = a - 0$

$5 = a$ $5 = a$

$a = 5$ $a = 5$

Solution 2)

$4 = - (a - 1)$ $4 = -(a - 1)$

$4 = - a + 1$ $4 = -a + 1$

$4 - 1 = - a + 1 - 1$ $4 - color(red)(1) = -a + 1 - color(red)(1)$

$3 = - a + 0$ $3 = -a + 0$

$3 = - a$ $3 = -a$

$- 1 \times 3 = - 1 \times - a$ $color(red)(-1) xx 3 = color(red)(-1) xx -a$

$- 3 = a$ $-3 = a$

$a = - 3$ $a = -3$

Solution: $a$ $a$ can be either $5$ $5$ or $- 3$ $-3$

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How do you find the value of a given the points (1,1), (a,1) with a distance of 4?

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