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3 years ago

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What is the midpoint and distance between points P(3,5) and Q(7,5)

1 answer:

storchak [24]3 years ago

4 0

The formula of a midpoint:

$M\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)$

The formula of a distance between two points:

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

We have the points P(3, 5) and Q(7, 5). Substitute:

$x=\dfrac{3+7}{2}=\dfrac{10}{2}=5\\\\y=\dfrac{5+5}{2}=\dfrac{10}{2}=5$

<h3>M(5, 5)</h3>

$d=\sqrt{(5-5)^2+(7-3)^2}=\sqrt{0^2+4^2}=\sqrt{4^2}=4$

<h3>Answer:</h3><h3>Midpoint = (5, 5)</h3><h3>Distance = 4</h3>

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Answer:

a. The critcal points are at

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b. Then, $x = -5$ is a maximum and $x=3$ is a minimum

c. The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

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(a)

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b.

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we will proceed to resolve each case to determine the solution

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If an ordered pair is the solution of the inequality, then it must satisfy the inequality.

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<u>Verify</u>

using a graphing tool

see the attached figure

the solution is the shaded area above the line

The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality

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