What is the distance of (–4, 7) and (–7, 8)?

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Answer 1 · 2017-06-15T19:11:11

$D (A, B) = \sqrt{10} \approx 3.1623$ $D(A,B)=sqrt(10)~~3.1623$

The distance between two points $A = (x_{1}, y_{1})$ $A=(x_1,y_1)$ and $B = (x_{2}, y_{2})$ $B=(x_2,y_2)$ is given by the distance formula.

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

We are given

$(x_{1}, y_{1}) = (- 4, 7)$ $(x_1,y_1)=(-4,7)$

and

$(x_{2}, y_{2}) = (- 7, 8)$ $(x_2,y_2)=(-7,8)$

Plugging these values into the distance formula gives:

$D (A, B) = \sqrt{{(- 7 - (- 4))}^{2} + {(8 - 7)}^{2}}$ $D(A,B)=sqrt((-7-(-4))^2+(8-7)^2)$

$D (A, B) = \sqrt{{(- 7 + 4)}^{2} + {(8 - 7)}^{2}}$ $D(A,B)=sqrt((-7+4)^2+(8-7)^2)$

$D (A, B) = \sqrt{{(- 3)}^{2} + {(1)}^{2}}$ $D(A,B)=sqrt((-3)^2+(1)^2)$

$D (A, B) = \sqrt{9 + 1}$ $D(A,B)=sqrt(9+1)$

$D (A, B) = \sqrt{10} \approx 3.1623$ $D(A,B)=sqrt(10)~~3.1623$