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miv72 [106K]
2 years ago
14

The points P(2, 1), Q(4, 5), and R(7, 4) are the midpoints of the sides of a triangle. Graph the three midsegments to form the m

idsegment triangle. Then use your graph and the properties of midsegments to draw the original triangle.
Mathematics
1 answer:
MariettaO [177]2 years ago
7 0

Answer:

  see attached

Step-by-step explanation:

We followed instructions to create the attached graph of the two triangles.

Each mid-segment is parallel to the side of the triangle whose midpoint is the vertex opposite that segment. So, we used a graphing tool to draw, for example, a line parallel to PQ through point R. The vertices of the original triangle are at the intersection points of these lines (or 1 mid-segment length from the midpoint).

__

Analytically, we can make use of the fact that each mid-segment is effectively a diagonal of a parallelogram. For example, PQ is a diagonal of APRQ. The other diagonal is AR. The two diagonals cross at the midpoint of each. This means we can find point A using the midpoint relation:

  midpoint AR = midpoint PQ

  (A +R)/2 = (P +Q)/2 . . . use the midpoint formula

  A +R = P +Q . . . . . . . . multiply by 2

  A = P +Q -R . . . . . . . . subtract R to get an expression for A

  A = (2, 1) +(4, 5) -(7, 4) = (2+4-7, 1+5-4) = (-1, 2)

The other vertices of ΔABC can be found in similar fashion:

  B = R +P -Q = (7, 4) +(2, 1) -(4, 5) = (7+2-4, 4+1-5) = (5, 0)

  C = Q +R -P = (4, 5) +(7, 4) -(2, 1) = (4+7-2, 5+4-1) = (9, 8)

So, the original triangle's vertices are ...

  A(-1, 2), B(5, 0), C(9, 8)

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Which expression is equivalent to cot t sec t?
Solnce55 [7]

Answer: csc(t)

Step-by-step explanation:

Alright, lets get started.

The given expression is given as :

cot( t) \times sec (t)

We know quotient identity as :

cot(t)=\frac{cos(t)}{sin(t)}

Similarly, we know reciprocal identity as :

sec(t)=\frac{1}{cos(t)}

lets plug the value of cot and sec in given expression

\frac{cos(t)}{sin(t)}  \times \frac{1}{cos(t)}

cos will be cancelled, remaining will be

\frac{1}{sin(t)}

Using reciprocal identity again, that will equal to :

csc(t)  ................... Answer (A)

8 0
3 years ago
Mai had $14.50. She spent $4.35 at the snack bar and $5.25 at the arcade. What is the exact amount of money mai has left​
velikii [3]

✧・゚: *✧・゚:*    *:・゚✧*:・゚✧

                  Hello!

✧・゚: *✧・゚:*    *:・゚✧*:・゚✧

❖ Mai has $4.90 left.

Add $4.35 and $5.25 to get the total amount that she spent:

$4.35 + $5.25 = $9.60

Then subtract to get the amount of money left:

$14.50 - $9.60 = $4.90

~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡

~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ

3 0
3 years ago
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Kyle and his friends share some apple pie equally. Each person gets 7/5 of the pies. Which of the following shows a possible way
stiv31 [10]

Answer:

7 apples divided among 5 people

Step-by-step explanation:

Given

Apple shared equally

Portion of each person = 7/5

Required

A possible way that shows how the pies were shared.

Given that 7/5 is the ration of the pie to each individual (Kyle and his friends).

Provided that each individual got equal ration....

The ration can be divided into two

The numerator = 7

The denominator = 5.

The numerator shows the number of things that were shared.

Hence, 7 apples were shared.

The denominator shows the number of people involved.

Hence, 5 people were involved.

So, we can conclude that 7 apples were divided among 5 people.

From option A through D, only option B satisfied this analysis

6 0
3 years ago
-7-7 (2m-7) = 7 (6+m)
levacccp [35]

Answer:

m= 0

Step-by-step explanation:

this is the right answer

-7-14m+49=42+7m

42-14m=42+7m

14m+7m=42-42

21m=0

m=0

4 0
3 years ago
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nadezda [96]
Y = 20x

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180/x = y

180/x = 20x

180 = 20x^2

x^2 = 6

x = + or - 3

Therefore y must equal + or - 60.
8 0
3 years ago
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