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viktelen [127]
3 years ago
10

Vanessa draws one side of equilateral ΔABC on the coordinate plane at points A(–2, 1) and B(4,1). What are the possible coordina

tes of vertex C? Select all that apply.
Mathematics
1 answer:
grandymaker [24]3 years ago
4 0

Important question. No menu of choices given so we'll just have to figure it out.

It's not possible in two dimensions for all three vertices of an equilateral triangle to be lattice points, i.e. points with integer coordinates.  

Since A(-2,1) and B(4,1) have integer coordinates, our other point won't. There will be a √3 involved, the algebraic tell that there's a 30/60/90 triangle lurking somewhere in the problem.

Here the given side is parallel to the x axis which makes things easier.  

|AB| = 4 - -2 = 6

The x coordinate of the third vertex will be the same as that of the midpoint of AB, let's call it M,

M = ( (-2 + 4) / 2, (1 + 1)/2 ) = (1, 1)

We're making some progress.  Whatever our height h is our two candidates for the third vertex C are (1, 1 ± h).

Since |AB|=6, we get |AB|=|BC|=|AC|=6 because it's an equilateral triangle.

The altitude CM bisects the triangle into 2 30/60/90 triangles.  Let's take one of them, AMC.  Angle AMC is a right angle, so we have a right triangle with legs |AM|=3 and |CM|=h, and hypotenuse |AC|=6. The Pythagorean Theorem tells us:

3² + h² = 6²

9 + h² = 36

h² = 27

h = 3√3

Answer: C is (1, 1 + 3√3) or (1, 1 - 3√3)

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Terrel lives 2 5/6 blocks away from his best friends house. His school is 4 1/3 blocks away in the same direction. If he stops a
Step2247 [10]

Answer:

5/8 of a mile

Step-by-step explanation:

Let the distance from Post Office to Friend's house =D

7/8 + 5/6 + D =miles - Total distance from Georgia's house to a Friend's house.

42 minutes / 18 minutes per mile =2 1/3 miles - total distance from her house to a friend's house. So, we have:

7/8 + 5/6 + D = 2 1/3, solve for D

[21 + 20] / 24 + D = 2 1/3

41/24 + D = 2 1/3                     subtract 41/24 from both sides

D =2 1/3 - 41/24

D =7/3 - 41/24

D =[56 -41] / 24

D = 15 / 24

D = 5/8 of a mile - the distance between the School and her Friend's house.

8 0
2 years ago
Solve each equation by finding all roots x^4-16=0
Alexandra [31]
Add both sides by 16
so you'll have x^4 =16
take the 4th root of both sides and you'll get x=  2
4 0
3 years ago
Read 2 more answers
In a right triangle, the hypotenuse is three inches more than twice the length of one leg. If the other leg is 12 inches, what i
andrew-mc [135]

Answer:

Length of hypothenuse = 13 inches

Length of other leg = 5 inches

Step-by-step explanation:

A triangle has three sides and three angles. A right angle triangle has 90 degrees as one of the angles. The remaining two angles are complimentary. This means that the sum if the other two angles is 90 degrees.

The longest side is the hypotenuse. The shorter sides are the opposite and adjacent.

In this triangle, the hypotenuse is three inches more than twice the length of one leg. Let the length of one leg be x inches.

Hypothenuse = 2x + 3

The other leg is 12 inches.

The diagram is illustrated in the attached photo.

Applying Pythagoras theorem,

Hypothenuse ^2 = adjacent^2 + opposite ^2

(2x+3)^2 = 12^2 + x^2

(2x+3)(2x+3)= 144 + x^2

4x^2 + 6x + 6x + 9 = 144 + x^2

4x^2 - x^2 + 6x + 6x + 9 - 144 = 0

3x^2 +12x - 135 = 0

3x^2 +27x - 15x - 135 = 0

3x(x+9)-15(x+9)=0

(3x -15)(x+9) = 0

3x -15 = 0 or x+9= 0

3x = 15 or x = -9

x = 15/3 = 5

x = 5inches because it cannot be negative.

Length of hypothenuse = 2x + 3

= 2×5 + 3 = 10 + 3 = 13 inches

6 0
3 years ago
A unique source of water pollution contributing to water quality problems in the Ganges River is: A. raw sewage. B. disease-caus
horrorfan [7]
Is this a multiple choice answer? If not, the answer is E. Ash from human cremations
6 0
2 years ago
The Big Dipper ice cream store charges 25 cents for a cone and 75 cents for each scoop of ice cream added to the cone. What will
yulyashka [42]
Double dip ice-cream cone = 25 + 2(75) = 175 cents = $1.75


Answer: $1.75
4 0
3 years ago
Read 2 more answers
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