1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Damm [24]
3 years ago
15

Laura is designing a rectangular porch for her house. On her scale drawing, the vertices of the rectangle are (2, 7), (8, 7), an

d (2, 9). What are the coordinates of the fourth vertex?

Mathematics
2 answers:
mote1985 [20]3 years ago
7 0

Answer:

Coordinates of fourth vertex are (8,9)  

Step-by-step explanation:

Given that Laura is designing a rectangular porch for her house. On her scale drawing, the vertices of the rectangle are (2, 7), (8, 7), and (2, 9).

we have to find the coordinates of the fourth vertex.

As diagonals of rectangle bisect each other and are congruent then the coordinates of E is the mid-point of AC as well as BD.

By mid-point formula if (a,b) and (c,d) are the coordinates of line segment then the coordinates of mid point are

(\frac{a+c}{2},\frac{b+d}{2})      

Mid-point of AC= mid point of BD

(\frac{a+2}{2},\frac{b+7}{2})=(\frac{8+2}{2},\frac{7+9}{2})

(\frac{a+2}{2},\frac{b+7}{2})=(5,8)

Comparing both sides , we get

\frac{a+2}{2}=5 and \frac{b+7}{2}=8

a+2=10 and b+7=16

a=8 and b=9

Hence, coordinates of fourth vertex are (8,9)    

Semenov [28]3 years ago
4 0
It has to be (8, 9) because that would put the 4th corner above (8, 7) and right of (2, 9).
You might be interested in
Find x, if the distance end points is (x,1) and (4,4) with the total distance is the square root of 10.
Alex Ar [27]
Okay, take a look at diagram 1 (I know it's rubbish I did it on paint :D), this shows all the information you've given in the question. The two coordinates and the distance between them.

Now if we draw additional lines on this diagram, we can make a right-angled triangle (this is on diagram 2). We can also work out the lengths of the additional sides because we know both coordinates at the end-points of the additional lines.

Finally because this is a right-angled triangle, Pythagoras' theorem must apply to its sides meaning
( \sqrt{10} )^2 = (x-4)^2 + 3^2
10 = (x-4)^2 + 9
(x-4)^2 = 1 \Rightarrow x-4 = 1
therefore x=5.

3 0
2 years ago
3x(x2 + 2x – 6) + 4(x2<br> – 6x + 2)
Drupady [299]

Step-by-step explanation:

3x(x2 + 2x – 6) + 4(x2

– 6x + 2)

4 0
2 years ago
Triangle ABC is an isosceles triangle, and side BC is congruent to side AC. If side AC equals 40 centimeters, and AB is one-half
Alik [6]

Answer:

100 cm

Step-by-step explanation:

Given:

AC = BC

AC = 40

2AB=AC

Simplify:

BC = 40

Simplify:

2AB = 40

Algebra:

AB = 20

Here's the sides:

AB = 20

AC = 40

BC = 40

Add all of them together:

100

8 0
2 years ago
Help Pls and Fast. correct answer gets brainliest<br> −8⋅f(0)+4⋅g(−8)
masha68 [24]

Answer:

-32

Step-by-step explanation:

Khanacademy

5 0
2 years ago
Which expression is equivalent to 3 √10x^5/54x^8
kolezko [41]
Is the last one
3√5/3x
8 0
3 years ago
Read 2 more answers
Other questions:
  • You find your dependent variable has a high degree of kurtosis. What is the first way to try to fix it?
    13·1 answer
  • Answers please!! I would do this but I don’t understand what statistical means..but if you do know what it means this is easy pe
    13·2 answers
  • researchers are conducting a survey about what brand of ice cream shoppers prefer. they survey the tenth person who walks into t
    15·2 answers
  • Combine like terms.<br> 8y – 4z + 3y + 5z = 11y + [? ]z
    6·1 answer
  • A model for my number has 6 ones blocks, 2 hundreds blocks and 3 tens blocks what number am i?
    5·1 answer
  • In the decimal system, when we divide a number by 10, the rightmost digit in the number is the remainder. Divide the number 157
    11·1 answer
  • 1.Which statement about two negative numbers is true? .
    7·2 answers
  • Plz help need this done by tomorrow thank you [Photo]​
    13·2 answers
  • Brainlyyyyyyyy just helppppppppppppppppppppppppppppppppppppppppppp
    9·2 answers
  • 2 A taxi charges $2.50 per mile in addition to a $2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!