Question 484041
Use the Pythagorean Theorem to find the distance between X(7,11) and Y(-1,5)


Let the third coordinate point of the right triangle be W.

If diagram is drawn, it’ll be seen that in order to get W (the third x-coordinate point of the right triangle), we simply subtract the smaller of the two x-coordinates from the larger. In this case, 7 – (- 1), or 7 + 1 = 8. We do the same for the y-coordinate, as follows: 11 – 5 = 6. 

This means that YW (horizontal line that’s parallel to the x-axis) has a length of 8, and XW (the vertical line that’s parallel to the y-axis) has a length of 6. 

With this, we can now find YX using the Pythagorean theorem. Therefore, we can say that:

{{{(YW)^2 + (XW)^2 = (XY)^2}}}
{{{8^2 + 6^2 = (XY)^2}}}
{{{64 + 36 = (XY)^2}}}
{{{100 = (XY)^2}}}
{{{sqrt(100) = XY}}}


10 = XY

Therefore, distance = XY = {{{highlight_green(10)}}} units


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Check
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The distance formula, {{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}}, can be used to verify the correctness of this answer. 


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