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a_sh-v [17]
3 years ago
15

I'm having a difficult time solving this . . . can someone please help me?! The map shows the route for a race. You are at A, wh

ich is 6000 feet from the first checkpoint B. The second checkpoint C is located at the midpoint between B and the end of the race D. The total race is 3 miles. How far apart are the 2 checkpoints? (Hint: There are 5280 feet in a mile.)
a)9840 feet
b)5280 feet
c)4920 feet
d)6000 feet ...?
Mathematics
1 answer:
Art [367]3 years ago
7 0
(C) is right option.Assuming the race is a straight line,then the whole race is 3x5280=15840feet.15840-6000=9840 is the distance from B to D9840/2=4920 is the distance from B to C.
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First of all, you can simplify the 4 at the numerator and the 14 at the denominator (they're both multiple of 2):

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Now, rationalize a denominator means that you have to get rid of the square root, in order to have an integer denominator.

To do so, remember that you can always multiply any number by 1 without changing its value, and you can always think of 1 as a fraction where numerator and denominator are equal:

\dfrac{2}{7\sqrt{2}} = \dfrac{2}{7\sqrt{2}}\cdot 1 = \dfrac{2}{7\sqrt{2}} \cdot \dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{2\sqrt{2}}{7\cdot 2} = \dfrac{\sqrt{2}}{7}

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Step-by-step explanation:

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Perhaps the easiest way to find the midpoint between two given points is to average their coordinates: add them up and divide by 2.

A) The midpoint C' of AB is
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The midpoint B' is
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The midpoint A' is
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B) The slope of the line between (x1, y1) and (x2, y2) is given by
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Using the values for A and A', we have
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The expression on the right has factors of (m+p) that cancel*, so we end up with
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* The only constraint is that (m+p) ≠ 0. Since m and p are both in the first quadrant, their sum must be non-zero and this constraint is satisfied.

The purpose of the exercise is to show that all three medians of a triangle intersect in a single point.
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Answer:

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Step-by-step explanation:

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