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viktelen [127]
2 years ago
11

Midpoint of the segment between the points (−5,13) and (6,4)

Mathematics
2 answers:
Leokris [45]2 years ago
6 0

Answer: (0.5,8.5)

Step-by-step explanation:

We need to use the following formula to find the Midpoint "M":

M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Given the points (-5,13) and (6,4) can identify that:

x_1=-5\\x_2=6\\\\y_1=13\\y_2=4

The final step is to substitute values into the formula.

Therefore, the midpoint of the segment between the points (-5,13) and (6,4) is:

M=(\frac{-5+6}{2},\frac{13+4}{2})\\\\M=(\frac{1}{2},\frac{17}{2})\\\\M=(0.5,8.5)

N76 [4]2 years ago
6 0

Answer:

(\frac{1}{2},\frac{17}{2})

Step-by-step explanation:

Midpoint formula is

( \frac{x + x_1}{2},\frac{y + y_1}{2})

The given points are,

(-5,13) and (6,4)

( \frac{-5 + 6}{2},\frac{13+4}{2})

( \frac{1}{2},\frac{17}{2})

Hence the midpoint of the segment between (-5,13) and (6,4) is

( \frac{1}{2},\frac{17}{2})

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The sin A is equal to 12/13 and the tan (A) is equal to 12/5.

<h3>RIGHT TRIANGLE</h3>

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: hypotenuse^2=(leg_1)^2+(leg_2)^2. And the main trigonometric ratios are:

sin(\beta )= \frac{opposite\;leg}{hypotenuse} \\ \\ cos(\beta )= \frac{adjacent\;leg}{hypotenuse} \\ \\ tan(\beta )= \frac{opposite\;leg}{adjacent\;leg} \\ \\

The question gives cos (A)=5/13. If cos (A) is represented by the quotient between the adjacent leg and the hypotenuse, you have:

adjacent leg=5

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Therefore, you can find the opposite leg of A from Pythagorean Theorem, see below.

hypotenuse^2=(leg_1)^2+(leg_2)^2\\ \\ 13^2=5^2+(leg_2)^2\\ \\ 169=25+(leg_2)^2\\ \\ 144=(leg_2)^2\\ \\ leg_2=12

Thus, the opposite leg is equal to 12. Now, you can find sin (A) since:

sin(A)= \frac{opposite\;leg}{hypotenuse}=\frac{12}{13}

Finally, you can find the tan (A) since:

tan(a )= \frac{opposite\;leg}{adjacent\;leg}=\frac{12}{5}

Learn more about trigonometric ratios here:

brainly.com/question/11967894

#SPJ1

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<h3>What is SAS?</h3>

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