All categories

2 years ago

Which point is a reflection of M(-5, -6) across the y-axis?

Mathematics

1 answer:

Fantom [35]2 years ago

3 0

Answer:

point R

Step-by-step explanation:

reflection rule for the y-axis

p(x, y)->p'(-x, y)

therefore:

M(-5, -6)->R(5, -6)

You might be interested in

In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm

tangare [24]

Answer:

$AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm$

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

$AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm$

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

$\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD$

Consider right triangle CAH.By the Pythagorean theorem,

$CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8$

The length cannot be negative, so CD=8 cm and

$CA=\sqrt{3}CD=8\sqrt{3}\ cm$

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

$AB=2CA=16\sqrt{3}\ cm$

By the Pythagorean theorem,

$BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm$

3 0

2 years ago

PLZZZZ HELPPPPPPP!!!!

Vladimir79 [104]

Answer: The height of the building is 50.75 feet.

Step-by-step explanation:

The ratio between the height of the object and the casted shadow must be equal for all the objects, as the angle at which the source if light impacts them is the same.

For the person, we know that it is 5.8ft tall, and the shadow is 3.2ft long.

The ratio will be: 5.8ft/3.2ft = 1.8125

Now, if H is the height of the building, and the shadow that the building casts is 28ft, we must have:

H/28ft = 1.8125

Now we can solve this for H.

H = 1.8125*28ft = 50.75 ft

Then the height of the building is 50.75 feet.

3 0

2 years ago

dear brainly, I hope you see this, Please be aware of when you go and delete a persons account and or questions and answers. Be

Scrat [10]

Answer: