What is the distance between $(1, 4)$ $(1, 4)$ and $(- 6, - 7)$ $(-6, -7)$ ?

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Answer 1 · 2018-04-16T23:59:07

$d = \sqrt{170}$ $d = sqrt(170)$

d= 13.04 units

To find the distance between points at $(1, 4)$ $(1,4)$ and $(- 6, - 7)$ $(-6,-7)$

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

for the points given
$x_{1} = 1$ $x_1 = 1$
$y_{1} = 4$ $y_1 = 4$
$x_{2} = - 6$ $x_2 = -6$
$y_{2} = - 7$ $y_2 = -7$

plugging in the values we get
$d = \sqrt{{(- 7 - 4)}^{2} + {(- 6 - 1)}^{2}}$ $d = sqrt((-7-4)^2 + (-6-1)^2)$

simplifying the parenthesis
$d = \sqrt{{(- 11)}^{2} + {(- 7)}^{2}}$ $d = sqrt((-11)^2 + (-7)^2)$

Simplifying the squares
$d = \sqrt{121 + 49}$ $d = sqrt(121 + 49)$

simplifying the radical
$d = \sqrt{170}$ $d = sqrt(170)$

d= 13.04 units

What is the distance between (1,4)(1, 4) and (−6,−7)(-6, -7)?