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3 years ago

Given the midpoint (1.5,1.5) and the endpoint (5,7) where is the other endpoint located

Mathematics

1 answer:

earnstyle [38]3 years ago

8 0

The formula of a midpoint:

$M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)$

We have:

$M(1.5,\ 1.5)\to x_M=1.5,\ y_M=1.5\\A(5,\ 7)\to x_A=5,\ y_A=7$

Substitute

$\dfrac{5+x_B}{2}=1.5\qquad|\cdot2\\\\5+x_B=3\qquad|-5\\\\x_B=-2\\\\\dfrac{7+y_B}{2}=1.5\qquad|\cdot2\\\\7+y_B=3\qquad|-7\\\\y_B=-4$

<h3>Answer: (-2, -4)</h3>

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Now we can use this radius in the equation:

$A=\pi (6)^{2}$

$A=36\pi$

Since all of the angles of each section are equal, we can assume that each of the sections has an equal area. There are 5 sections, so we need to divide $36 \pi$ by 5 to find the area of each section:

$\frac{36 \pi}{5} =7.2 \pi$

Each section has an area of $7.2\pi units^{2}$ or, using 3.14 for pi, $7.2*3.14=22.61units^{2}$ .

Since we are told to find the area of the blue sections, we know that there are 2 sections that are blue. So we need to multiply the area of each section by 2, to find the area of two of the sections:

$22.61*2=45.22units^{2}$

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