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
In-s [12.5K]
3 years ago
13

Given: The coordinates of triangle PQR are P(0, 0), Q(2a, 0), and R(2b, 2c).

Mathematics
1 answer:
masha68 [24]3 years ago
6 0

Answer:

The line containing the midpoints of two sides of a triangle is parallel to the third side ⇒ proved down

Step-by-step explanation:

* Lets revise the rules of the midpoint and the slope to prove the

  problem

- The slope of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

- The mid-point of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

* Lets solve the problem

- PQR is a triangle of vertices P (0 , 0) , Q (2a , 0) , R (2b , 2c)

- Lets find the mid-poits of PQ called A

∵ Point P is (x1 , y1) and point Q is (x2 , y2)

∴ x1 = 0 , x2 = 2a and y1 = 0 , y2 = 0

∵ A is the mid-point of PQ

∴ A=(\frac{0+2a}{2},\frac{0+0}{2})=(\frac{2a}{2},\frac{0}{2})=(a,0)

- Lets find the mid-poits of PR which called B

∵ Point P is (x1 , y1) and point R is (x2 , y2)

∴ x1 = 0 , x2 = 2b and y1 = 0 , y2 = 2c

∵ B is the mid-point of PR

∴ B=(\frac{0+2b}{2},\frac{0+2c}{2})=(\frac{2b}{2},\frac{2c}{2})=(b,c)

- The parallel line have equal slopes, so lets find the slopes of AB and

  QR to prove that they have same slopes then they are parallel

# Slope of AB

∵ Point A is (x1 , y1) and point B is (x2 , y2)

∵ Point A = (a , 0) and point B = (b , c)

∴ x1 = a , x2 = b and y1 = 0 and y2 = c

∴ The slope of AB is m=\frac{c-0}{b-a}=\frac{c}{b-a}

# Slope of QR

∵ Point Q is (x1 , y1) and point R is (x2 , y2)

∵ Point Q = (2a , 0) and point R = (2b , 2c)

∴ x1 = 2a , x2 = 2b and y1 = 0 and y2 = 2c

∴ The slope of AB is m=\frac{2c-0}{2b-2a}=\frac{2c}{2(b-c)}=\frac{c}{b-a}

∵ The slopes of AB and QR are equal

∴ AB // QR

∵ AB is the line containing the midpoints of PQ and PR of Δ PQR

∵ QR is the third side of the triangle

∴ The line containing the midpoints of two sides of a triangle is parallel

  to the third side

You might be interested in
PLSS HELP!! NEED ASAP!!! MARKING BRAINLIEST!!! PLS EXPLAIN!!! At the produce store you can buy 4 bags of bananas for $22.52. How
alexdok [17]

Step-by-step explanation:

4 bags of bananas for $22.52

=> 2 bags of bananas for $22.52 * 2/4 = $11.26.

Hence it would cost $11.26.

5 0
3 years ago
Simplify: 7!<br> 5,040<br> 40,320<br> 7<br> 720
Arturiano [62]
5040, I looked up the factorial of 7
8 0
3 years ago
Read 2 more answers
the expression 5n can be. used to find the total cost in dollars of bowling where n is the number of games bowled and 2 represen
sergiy2304 [10]
17 dollars for Vincent to bowl 3 gamees
4 0
3 years ago
Read 2 more answers
Please answer this correctly
Lynna [10]

Answer:

75%

Step-by-step explanation:

There is 1 whisker and quartiles 1-3 so:

25%+25%+25%=75%

6 0
2 years ago
2x + y + z when x= -2 and y=3 z=5
ruslelena [56]

Answer:4

Step-by-step explanation:2x+y+z=2(-2)+3+5=(-4)+3+5=(-1)+5=4

6 0
3 years ago
Read 2 more answers
Other questions:
  • 4 1/8 c = __ fl oz help plz
    6·1 answer
  • As an estimation we are told £3 is €4.<br> Convert €20 to pounds.
    9·1 answer
  • There are many penguins on a hill. 53 penguins waddled off the hill. Now 21 penguins remain on the hill. How many penguins were
    14·2 answers
  • A rectangle has an area of 24 square units and a side length of 234 units. Find the other side length of the rectangle.
    5·1 answer
  • Y varies directly with x. When x is 4 y is 8. Find y when x = 10.
    9·1 answer
  • Can anybody help me with this question<br> Show that 4x + 4 = 28
    14·2 answers
  • A team manager buys a team jacket and a team cup for each of the 10 players on the dodgeball team. Each team cup costs $10.70. T
    9·1 answer
  • Here you go ☺️ I NEED HELP SO HELP PLS
    10·2 answers
  • What is the standard form equation of the line shown below?
    14·2 answers
  • .................................
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!