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
nalin [4]
3 years ago
5

Lamar is writing a coordinate proof to show that a segment from the midpoint of the hypotenuse of a right triangle to the opposi

te vertex forms two triangles with equal areas. He starts by assigning coordinates as given.
A right triangle is graphed on a coordinate plane. The horizontal x-axis and y-axis are solid, and the grid is hidden. The vertices are labeled as M, K, and L. The vertex labeled as M lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as K lies on begin ordered pair 0 comma 2 b end ordered pair. The vertex labeled as L lies on begin ordered pair 2a comma 0 end ordered pair. A bisector is drawn from point M to the line KL. The intersection point on line KL is labeled as N.

Enter the answers to complete the coordinate proof.
N is the midpoint of KL¯¯¯¯¯KL¯ . Therefore, the coordinates of N are (a,
).

To find the area of △KNM△KNM , the length of the base MK is 2b, and the length of the height is a. So an expression for the area of △KNM△KNM is
.

To find the area of △MNL△MNL , the length of the base ML is
, and the length of the height is
. So an expression for the area of △MNL△MNL is ab.

Comparing the expressions for the areas shows that the areas of the triangles are equal.

Mathematics
2 answers:
Zanzabum3 years ago
6 0

1. N is a midpoint of the segment KL, then N has coordinates

\left(\dfrac{x_K+x_L}{2},\dfrac{y_K+y_L}{2} \right) =\left(\dfrac{0+2a}{2},\dfrac{2b+0}{2} \right) =(a,b).

2. To find the area of △KNM, the length of the base MK is 2b, and the length of the height is a. So an expression for the area of △KNM is

A_{KMN}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}=\dfrac{1}{2}\cdot 2b\cdot a=ab.

3. To find the area of △MNL, the length of the base ML is 2a and the length of the height is b. So an expression for the area of △MNL is

A_{MNL}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}=\dfrac{1}{2}\cdot 2a\cdot b=ab.

4. Comparing the expressions for the areas you have that the area A_{KMN} is equal to the area A_{MNL}. This means that the segment from the midpoint of the hypotenuse of a right triangle to the opposite vertex forms two triangles with equal areas.

Elanso [62]3 years ago
3 0
The coordinates of N is (a,b) using the midpoint formula.
The area for <span>△KNM is (1/2)(a)(2b) = ab
</span><span>The area of △MNL is ab.
Since the area of </span>△KNM = △MNL and the area of △KML is 2ab, then we have proved that <span>a segment from the midpoint of the hypotenuse of a right triangle to the opposite vertex forms two triangles with equal areas.</span>
You might be interested in
The base of an isosceles triangle is one and a half times the length of the other two sides. A smaller triangle has a perimeter
stira [4]

Answer:

P = 1.5x.

Step-by-step explanation:

Let the length of each side of the first triangle be x, then

Perimeter of this triangle

= 2x + 1.5x

= 3.5x.

So perimeter of smaller triangle is:

P = 1/2 * 3.5x

P = 1,.5x.

5 0
3 years ago
twice the difference of a number and 7 is equal to three times the sum of the number and 7. find the number​
otez555 [7]

Answer:

- 35  

Step-by-step explanation:

2(x - 7) = 3(x+7)

2x - 14 = 3x + 21

- 21 - 14 = 3x - 2x

x = - 35  

Rechecking :

2(-35 - 7) = 3 (-35 +7)

- 84 = - 84

I hope im right!!!

7 0
3 years ago
Xavier, Yolanda and Sara shared some money. Yolanda received 40% more money than Xavier, and Zara received 60% of Yolanda's shar
leonid [27]

Answer:

Step-by-step explanation:

Xavier, Yolanda and Zara shared some money.

Let x represent Xavier's share

Let y represent Yolanda's share

Let z represent Zara's share.

Yolanda received 40% more money than Xavier. This means that

y = x + 40/100×x = x + 0.4x = 1.4x

Zara received 60% of Yolanda's share. This means that

z = 60/100× 1.4 = 0.6×1.4 = 0.84x

. If Zara received $1,176, then,

0.84x = 1176

x = 1176/0.84 = 1400

y = 1.4 × 1400 = $1960

z = 0.84 × 1400 = $1176

The sum of the money is

1400 + 1960 + 1176 = $4536

6 0
3 years ago
Plz help with this question​
Dennis_Churaev [7]

Answer:

y = -2x+4

Step-by-step explanation:

the equation of the line there is: y = -2x+8

The parallel line to this one should have the same slope as the first one(-2x)

Parallel lines always have the same slopes

7 0
3 years ago
Aimee and Ben are purchasing a condominium and are financing $415,500. The mortgage is a 20-year 3/1 ARM at 2.75% with a cap str
Sonbull [250]
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

 <span>Bart and April are purchasing a house with a 15-year, 2/1 ARM for $315,000 at 5.85% with a 2/8 cap structure. What will the difference in payments be from year 2 to year 3? 

$333.68 </span>
4 0
3 years ago
Other questions:
  • (X^4+5x^2-36)(2x^2+9x-5)=0 solve for the roots. Factor both quadratic equations
    15·2 answers
  • A jar contains 4 brown marbles and 9 yellow marbles.
    9·2 answers
  • Which unit rate corresponds to the proportional relationship shown in the graph? Drag and drop the answer into the box to match
    6·2 answers
  • 1/3(6z+7.2)=0.5(8z+2)-0.4 please hurry this is for now
    8·1 answer
  • Derivative of 2 tan^3(x)+5 csc^4(x) ?
    10·1 answer
  • Ramon drove 425 miles on 15 1/2 of gas. How many miles per gallon did he drive?
    5·2 answers
  • On a coordinate plane, 2 cube root functions are shown. The first cube root function is a solid line and goes through (negative
    8·2 answers
  • A company borrows $50,000 for 8 years at a simple interest rate of 13.5%. Find the interest paid on the loan and the total amoun
    5·1 answer
  • Bill drove 605 miles in 11 hours. At the same rate, how many miles would he drive in 5 hours?
    14·2 answers
  • Which term could be put in the blank to create a fully simplified polynomial written in standard form?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!