All categories

4 years ago

11. Mis the midpoint of QR. Q is at (-8, 2) and M is at (4, -3). Find the coordinates of the endpoint R.

Mathematics

1 answer:

tamaranim1 [39]4 years ago

8 0

Answer:

R(16,-8)

Step-by-step explanation:

if (x1,y1) and (x2,y2) are coordinates of two points and (x,y) the coordinate of midpoint.

then x=(x1+x2)/2

and y=(y1+y2)/2

let coordinates of R are (x,y)

4=(-8+x)/2

8=-8+x

x=8+8=16

-3=(2+y)/2

-6=2+y

y=-6-2=-8

so R is (16,-8)

You might be interested in

Someone help fast! please

Lera25 [3.4K]

Answer:

48cm

Step-by-step explanation:

96/12=8

This means that 8 is the factor by which the diagram and the actual ramp vary

so then you multiply 8 times the height on the diagram to find the true height

8x6=48

6 0

3 years ago

Please help this is confusing.

Makovka662 [10]

Answer:

The mashi e drilled down 45 feet. So -45

Step-by-step explanation:

72 = 24h

X = 15h

24x = 1080

x = 45

7 0

3 years ago

Someone Please help me.

Lady_Fox [76]

Answer:

-2

Step-by-step explanation:

rise over run

$\frac{rise (-2)}{run 1}$

3 0

4 years ago

Read 2 more answers

If D is midpoint of side BC of triangle ABC. P and Q are points lying respectively on side AB and AC such that DP is parallel to

LUCKY_DIMON [66]

See proof below

Step-by-step explanation:

Assume triangle ABC to have vertices at;

A(2,-1), B(2,-7) and C(6,-7)

D is midpoint of BC, thus D is at (4,-7)

The P and Q, are lying on side AB and AC, hence assume P is at (2,-4) and Q is at (4,-4) such at DP is parallel to QA

Plot the points on a graph tool and join the points to view the sketch.

To prove area of triangle CPQ is 1/4 area of ABC will be;

Find area ABC and CPQ then compare the areas.

Apply the distance formula to find the length of sides of the triangles then find the areas.

The distance formula is;

$d=\sqrt{x_2-x_1)^2+(y_2-y_1)^2}$

Length of side AB from the sketch is;

$AB=\sqrt{(2-2)^2+(-7--1)^2} =\sqrt{-6^2} =\sqrt{36} =6units$

Length of side BC will be;

$BC=\sqrt{(-7--7)^2+(6-2)^2} =\sqrt{4^2} =\sqrt{16} =4units$

Thus area of triangle ABC will be;

1/2 *base length*height ------because it is a right-triangle

1/2*4*6=12 square units

Find the lengths of all sides of triangle CPQ

Length of side PQ is half that of side BC thus PQ=2 units

Length of side PC is;

$PC=\sqrt{(6-2)^2+(-7--4)^2} =\sqrt{4^2+-3^2} =\sqrt{16+9} =\sqrt{25} =5units$

Length of side QC will be;

$QC=\sqrt{(6-4)^2+(-7--4)^2} =\sqrt{2^2+-3^3} =\sqrt{4+9} =\sqrt{13}$

QC= √13 = 3.6 units

Find area of triangle CPQ given all sides by applying the Heron's formula for area of triangle which is;

A=√s(s-a)(s-b)(s-c) where;

A=area of the triangle

s= half the perimeter of the triangle

a=side PQ = 2 units

b=side PC = 5 units

c= side QC = 3.6 units

Finding the perimeter of triangle CPQ will be;

P=sum of all sides

P=2+5+3.6 =10.6 units

s=10.6/2 = 5.3

Area of the triangle CPQ will be;

$A=\sqrt{5.3(5.3-2)(5.3-5)(5.3-3.6)} \\A=\sqrt{5.3(3.3)(0.3)(1.7)} \\A=\sqrt{8.9} =2.98$

A=3.0 (1 decimal place)

Compare the areas;

Area of triangle ABC=12 square units

Area of triangle CPQ = 3 square units

Area of triangle CPQ / Area of triangle ABC = 3/12 =1/4

Thus you have proved that area of triangle CPQ is 1/4 th area of triangle ABC because 1/4 *12 =3

Learn More

Area of a triangle ;brainly.com/question/14869984

The Heron's formula : brainly.com/question/10713495

Keywords: midpoint, triangle, sides, parallel, prove , area, equal

#LearnwithBrainly

6 0

3 years ago

Horizontal lines ℓ and m are parallel. Line m is 9 units below line . ℓ . Both lines are translated 5 units left and 4 units dow

Lelu [443]

Answer:

9 unit

Step-by-step explanation:

after a translation the distance between the lines has no change.

5 0

3 years ago

11. Mis the midpoint of QR. Q is at (-8, 2) and M is at (4, -3). Find the coordinates of the endpoint R.​

11. Mis the midpoint of QR. Q is at (-8, 2) and M is at (4, -3). Find the coordinates of the endpoint R.