Question

Find the distance between (-12, 1) and (12, -1).

Answer 1

If the coordinates of two points are (x_1,y_1) and (x_2,y_2), the distance between them is given by the formula:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}`

Substitute for the coordinates: (-12,1) and (12,-1):

`\begin{gathered} d=\sqrt[]{(12-(-12))^2+(-1-1)^2} \\ =\sqrt[]{(12+12)^2+(-2)^2} \\ =\sqrt[]{(24)^2+4} \\ =\sqrt[]{576+4} \\ =\sqrt[]{580} \\ =2\cdot\sqrt[]{145} \\ \approx24.08318916\ldots \end{gathered}`

Therefore, the distance between (-12,1) and (12,-1) is approximately 24.08.