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noname [10]
3 years ago
5

Find the perimeter of a triangle with points A(1,2), B(1,8), and C(5,5) on a Cartesian coordinate plane.

Mathematics
1 answer:
Assoli18 [71]3 years ago
7 0

Check the picture below.

the distance from 1,2 to 1,8 is simply 6 units, we can read that off the grid.  Now let's see what the other distances are, and add them all up to get the perimeter.

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AC=\sqrt{(5-1)^2+(5-2)^2}\implies AC=\sqrt{4^2+3^2} \\\\\\ AC=\sqrt{25}\implies AC=5 \\\\[-0.35em] ~\dotfill

\bf B(\stackrel{x_1}{1}~,~\stackrel{y_1}{8})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{5}) \\\\\\ BC=\sqrt{(5-1)^2+(5-8)^2}\implies BC=\sqrt{4^2+3^2} \\\\\\ BC=\sqrt{25}\implies BC=5 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{perimeter}{6+5+5\implies 16}~\hfill

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3 years ago
6 people consists of 3 married couples. Each couple wants to sit with older partner on the left.
Lera25 [3.4K]

a. The first part asks for how many ways they can be seated together in a row. Therefore we want the permutations of the set of 6 people, or 6 factorial,

6! = 6 * 5

= 30 * 4

= 360 * 2 = 720 possible ways to order 6 people in a row

b. There are two cases to consider here. If the doctor were to sit in the left - most seat, or the right - most seat. In either case there would be 5 people remaining, and hence 5! possible ways to arrange themselves.

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= 20 * 3

= 120 * 1 = 120 possible ways to arrange themselves if the doctor were to sit in either the left - most or right - most seat.

In either case there are 120 ways, so 120 + 120 = Total of 240 arrangements among the 6 people if the doctor sits in the aisle seat ( leftmost or rightmost seat )

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8 0
3 years ago
A) Using theorems pertaining to transverals and parallel lines, prove that m∠1 + m∠2 = 180o
PtichkaEL [24]
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5 0
3 years ago
(a) use the pythagorean theorem to determine the length of the unknown side of the triangle, (b) determine the perimeter of the
Kisachek [45]

Answer:

(A) 40 km

(B) 90 km

(C) 180 km²

Step-by-step explanation:

To find the missing side of this triangle, let's use the Pythagorean theorem.

a^2+b^2=c^2, assuming that a and b are legs, and c is the hypotenuse.

Assuming the 9km side is a, we need to find the value of b, so we can substitute into the equation.

9^2+b^2=41^2\\81+b^2=1681\\b^2=1681-81\\b^2=1600\\\\b = \sqrt{1600} \\b=40

So, the length of the missing side is 40. Now that we know this piece of information, we can find the perimeter and area of the triangle.

The perimeter is all the sides added together, so 41+9+40 = 90 km is the perimeter.

The area are the two legs multiplied divided by 2.

So,

\frac{9\cdot40}{2} \\\\\frac{360}{2}\\\\180

So the area of this triangle is 180 cm²

I hope this helped!

8 0
3 years ago
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iogann1982 [59]

Answer:

well the shape is same but the measurements are different

Step-by-step explanation:

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