How do you find the value of a given the points (4,a), (1,6) with a distance of 5?

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Answer 1 · 2016-07-27T12:18:46

$a = 10 or a = 2$ $a = 10 or a=2$

Use the distance formula and substitute the values you know:

$| A B | = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $|AB| = sqrt[(x_2-x_1)^2 +(y_2-y_1)^2]$

$5 = \sqrt{{(4 - 1)}^{2} + {(a - 6)}^{2}}$ $5 = sqrt[(4-1)^2 +(a-6)^2$

$5 = \sqrt{3^{2} + {(a - 6)}^{2}} square both sides$ $5 = sqrt[3^2 +(a-6)^2]" square both sides"$

$25 = 9 + (a^{2} - 12 a + 36) quadratic = 0$ $25 = 9 + (a^2 -12a +36)" quadratic = 0"$

$0 = a^{2} - 12 a + 36 + 9 - 25$ $0 = a^2 -12a +36 +9 -25$

$0 = a^{2} - 12 a + 20$ $0 = a^2 -12a +20$

Now solve the quadratic to find two possible answers for a.

$0 = (a - 10) (a - 2)$ $0= (a-10)(a-2)$

This gives the possible answers for a as;
$a = 10 or a = 2$ $a = 10 or a=2$