All categories

3 years ago

B is the midpoint of AC and E is the midpoint of BD. If A (-9, -4), C (-1,6) and E (-4, 3), find the coordinates of D

Mathematics

1 answer:

Anettt [7]3 years ago

7 0

The coordinates of D are (-3, -7)

First we need to find the coordinates of B. In order to do that we simply take the average of the two points that make up the segment for which it is the midpoint (A and C).

Average of x's

-9 + -1 = -10/2 = -5

Average of y's

-4 + 6 = 2/2 = 1

Therefore, the coordinates of B are (-5, 1).

Now we can find D by noting the E will be the average of B and D. So we can use the average equation to determine the values of D.

Average of x's

(B + D)/2 = E

(-5 + D)/2 = -4

-5 + D = -8

D = -3

Average of y's

(B + D)/2 = E

(1 + D)/2 = -3

1 + D = -6

D = -7

Now we know the coordinates of D to be (-3, -7)

You might be interested in

Richie spent $120 on 12 rose bushes and 2 gardenias, while Jim spent it $150 on 10 rose bushes and 10 gardenias. What is the cos

Basile [38]

With the given information, we can create several equations:

120 = 12x + 2y
150 = 10x + 10y

With x being the number of rose bushes, and y being the number of gardenias.

To find the values of the variables, we can use two methods: Substitution or Elimination

For this case, let us use elimination. To begin, let's be clear that we are going to be adding these equations together. Therefore, in order to get the value of one variable, we must cancel one of them out - it could be x or y, it doesn't matter which one you decide to cancel out. Let's cancel the x out:

We first need to multiply the equations by numbers that would cause the x's to cancel out - and this can be done as follows:

-10(120 = 12x + 2y)
12(150 = 10x + 10y) => Notice how one of these is negative

Multiply out:

-1200 = -120x - 20y
+ 1800 = 120x + 120y => Add these two equations together
---------------------------------
600 = 100y

Now we can solve for y:

y = 6

With this value of y known, we can then pick an equation from the beginning of the question, and plug y in to solve for x:

120 = 12x + 2y => 120 = 12x + 2(6)

Now we can solve for x:

120 = 12x + 12 => 108 = 12x

x = 9

So now we know that x = 9, and y = 6.

With rose bushes being x, we now know that the cost of 1 rose bush is $9.
With gardenias being y, we now know that the cost of 1 gardenia is $6.

4 0

2 years ago

(r-3)(r-1)<br> Help me please!!!

madreJ [45]

Answer:

= r²−4r+3

Step-by-step explanation:

(r - 3) (r - 1)

(r x r) + (r x -1) + (-3 x r) + (-3 x -1)

r² + - r - 3r + 3

= r²−4r+3

5 0

2 years ago

There are 12 students in a homeroom wearing a school t-shirt these students make up 60% of the class how many students are in th

Yuki888 [10]

Answer:

there is a total of 20 students in the class because 60% of 20 is 12

Step-by-step explanation:

pls answer my recent question :(

7 0

2 years ago

HEEEEEELLLLLLLLPPPPPPPPPPPPP-2/3+1/3

motikmotik

Answer:

the total will be 1

Step-by-step explanation:

ok so the denomitor are matching so you can add straight across

1/3 +2/3 = 3/3

3/3 = 1 whole so there fore your answer is 1

Angie<3 have the best of best day today

6 0

2 years ago

A circle is the set of all points that are the same distance from one given point. find an example that contradicts this definit

lyudmila [28]

The accurate definition is that the circle that's closest to the 2 dimensional figure where all the set of point in the plane should be equal distance.

<h3>How to illustrate a circle?</h3>

A circle simply means the set of all the points that are the same distance from a given point.

In this case, the contradiction is that the definition should be applied to three dimensional space so that it will be a sphere.

The accurate definition is that the circle that's closest to the 2 dimensional figure where all the set of point in the plane should be equal distance. A example is a point or line.

Learn more about circle on:

brainly.com/question/24375372

#SPJ1

4 0

1 year ago