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4 years ago

If A = (-2, -4) and B = (-8, 4), what is the length of AB?

Mathematics

2 answers:

svetoff [14.1K]4 years ago

5 0

Answer: OPTION D

Step-by-step explanation:

To solve this exercise you must use the formula for calculate the distance between two points, which is shown below:

$d_{(A,B)}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Now, you must substitute the points given in the problem into the formula:

A(-2,-4)

B(-8,4)

$d_{(A,B)}=\sqrt{(-8-(-2))^2+(4-(-4))^2}$

Then, the result is:

$d_{(A,B)}=10units$

mars1129 [50]4 years ago

4 0

Answer:

Choice D is correct answer.

Step-by-step explanation:

We have given two points.

A = (-2, -4) and B = (-8, 4)

We have to find length of AB.

We use distance formula to find distance between two points.

d = √(x₂-x₁)²+(y₂-y₁)²

Let A = (x₁,y₁) = (-2, -4) and B = (x₂,y₂) = (-8, 4)

Putting above values in formula, we have

d = √(-8-(-2))²+(4-(-4))²

d = √(-8+2)²+(4+4)²

d = √(-6)²+(8)²

d = √36+64

d = √100

d = 10 units

Hence , The length of AB is 10 units.

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Altitudes $\overline{ax}$ and $\overline{by}$ of acute triangle $abc$ intersect at $h$. if $\angle ahb = 132^\circ$, then what i

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Answer: 48 degrees

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See the attached image for a visual of the problem and answer.

Based on the diagram, we have angle AHB = 132 degrees (given) equal in measure to angle XHY since these two angles are vertical angles.

Angles HYC and HXC are right angles due to the nature of AX and BY being altitudes. Recall that altitudes are segments that go from one vertex to the opposite side and they are perpendicular to the opposite side.

Focus on quadrilateral HXCY. So far, we know that...
Angle XHY = 132 degrees
Angle HYC = 90 degrees
Angle HXC = 90 degrees

The angle we want to find is angle ACB, which is the same as angle YCX. This angle is the missing angle of the quadrilateral HXCY.

For any quadrilateral, the four angles must add to 360 degrees.

(angle XHY) + (angle HYC) + (angle HXC) + (angle YCX) = 360
(132) + (90) + (90) + (angle YCX) = 360
312 + (angle YCX) = 360
312 + (angle YCX) - 312 = 360 - 312
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Since angle ACB is the same as angle YCX, we can say
angle ACB = angle YCX = 48 degrees

So in summary,
angle ACB = 48 degrees

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4 years ago

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Step-by-step explanation:

There are two ways you can solve this. One is with the Pythagorean identity:

sin²θ + cos²θ = 1

The other way is by knowing your unit circle.

1. From the unit circle, we know that cos θ = 1/2 at θ = π/3 and θ = 5π/3. Since θ is in Quadrant IV, then θ = 5π/3. sin (5π/3) = -(√3)/2.

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We can repeat these steps for the other questions.

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Step-by-step explanation:

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