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Kisachek [45]
3 years ago
5

The coordinates A(2, 1), B(7, 1), C(2, 4) form what type of polygon?

Mathematics
2 answers:
MAVERICK [17]3 years ago
4 0

Answer:  The correct option is (C) a right triangle.

Step-by-step explanation:  The given co-ordinates of a polygon are A(2, 1), B(7, 1), C(2, 4).

We are to select the correct type of the polygon.

Since we have the co-ordinates of the three points A, B and C, so the polygon will surely be a triangle.

Now, the lengths of the three sides AB, BC and CA of ΔABC can be calculated using distance formula as follows :

AB=\sqrt{(7-2)^2+(1-1)^2}=\sqrt{25+0}=\sqrt{25}=5,\\\\BC=\sqrt{(2-7)^2+(4-1)^2}=\sqrt{25+9}=\sqrt{34},\\\\CA=\sqrt{(2-2)^2+(1-4)^2}=\sqrt{0+9}=\sqrt{9}=3.

We have

AB^2+CA^2=5^2+3^2=25+9=34,\\\\BC^2=(\sqrt{34})^2=34.

This implies that

AB^2+CA^2=BC^2,

which is the Pythagorean triple. Hence, triangle ABC is a right-angled triangle.

Thus, (C) is the correct option.

Vesnalui [34]3 years ago
3 0
It appears to be a right triangle.
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Laura lives 15 miles east of Kevin’s place. Kevin lives 8 miles south of Michelle’s place. How far does Michelle live from Laura
My name is Ann [436]

Answer:

17 miles.

Step-by-step explanation:

Let's define:

North as the positive y-axis

East as the positive x-axis.

We know that Laura lives 15 miles east of Kevin's place.

Kevin lives 8 miles south of Michelle's place.

So, if we define the origin, (0, 0) as Laura's place.

From:

"that Laura lives 15 miles east of Kevin's place."

We have that the location of Kevin's house is 15 miles west from Laura's place, then Kevin's house is at:

(0, 0) + (-15mi, 0) = (-15mi, 0)

From Kevin lives 8 miles south of Michelle's place, we know that Michelle's live 8 miles north of Kevin's place.

Then the location of Michele's house is the location of Kevin's plus (0, 8mi).

Michelle's house is located at:

(-15mi, 0) + (0, 8mi)  =(-15mi, 8mi)

Now we want to find the distance between Michelle's house and Laura's house.

Michelle's house is at (-15mi, 8mi)

Laura's house is at (0mi, 0mi)

Remember that the distance between two points (a, b) and (c, d) is given by:

D = \sqrt{(a - c)^2 + (b - d)^2}

Then the distance between  (-15mi, 8mi) and (0mi, 0mi) is:

D = \sqrt{(-15mi - 0mi)^2 + (8mi - 0mi)^2} = 17mi

The correct option is the first one, 17 miles.

6 0
3 years ago
I am a number between 10 and 25. I am a multiple of 8 and one of my digits is 2 what number am I?
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Step-by-step explanation:

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Next door to me lives a man with his son. They both work in the same factory. I watch them going to work through my window. The
kirza4 [7]

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Answer:

  k = 5

Step-by-step explanation:

Suppose the distance to the factory is 1 unit. Then the speed the father walks is ...

  speed = distance/time = 1 / 30 . . . . units per minute

When the father leaves 10 minutes earlier than the son, his position t minutes after the son starts walking is ...

  d = 1/30(t +10)

Similarly, when the father starts 5 minutes earlier than the son, his position t minutes after the son starts walking is ...

  d = (1/30)(t +5)

We want that to be the same as the distance the son covers t minutes after he starts walking. The son's progress is ...

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To find the value of k such that the distance covered is the same 2k minutes after the son starts, we will use t=2k and d=d, so ...

  (1/30)(2k +5) = (1/20)(2k)

  4k +10 = 6k . . . . . multiply by 60

  10 = 2k . . . . . . . . . subtract 4k

  5 = k . . . . . . . . . . . divide by 2

__

The attached graph shows the different scenarios, where the blue line is the son's progress. When the father starts 5 minutes earlier, the son meets him half-way to the factory after 10 minutes, so k = 10/2 = 5.

5 0
3 years ago
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