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Question 71414: find the distance d(A,B) between the points A(-1,0) and B(4,3).
Thanks
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! find the distance d(A,B) between the points A(-1,0) and B(4,3).
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There is a Distance formula for getting the answer. That formula says:
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In this case you can choose to identify point B as point 2 and point A as point 1. Doing that
makes y2 =3, x2 = 4, y1 = 0, and x1 = -1. Now all you have to do is to plug these values
into the equation and solve as follows:
.
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The answer is that the distance between the points is  .
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You don't have to memorize the formula, if you think about it. It is just the Pythagorean
theorem for a right triangle. One leg of the triangle is the horizontal or x distance
between the points and the other leg is the vertical or y distance between the points.
The hypotenuse then becomes the distance between the points which is what you are looking
for. Put a couple of points on a graph. Then call one of the points point 1 and the other
point 2. Draw a horizontal line through one of the points and draw a vertical line through
the other point. Finally, draw a line connecting the two points. Notice how a right
triangle is formed. Use the Pythagorean theorem to find the distance between the points
which as you will see is the hypotenuse of the right triangle you have formed. Recall that
the Pythagorean theorem says:
.
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where A is one leg of the right triangle, B is the other leg, and C is the hypotenuse.
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This, to me, is the easy way to look at this problem, but you certainly can memorize
the distance formula if you find that easier.
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Hope this helps with how to understand and solve this problem.
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