All categories

2 years ago

Triangle ABC has vertices A(–2, –3), B(–5, –3), and C(–4, –2). The triangle is rotated 90° counterclockwise around the origin.

Mathematics

2 answers:

Yuri [45]2 years ago

5 0

Answer:B

Step-by-step explanation:B

Mama L [17]2 years ago

4 0

The answer is the option B: A'(3, -2), B'(3, -5), C'(2, -4).

The explanation is shown below:

1. You must apply the following rule of rotation when the figure is rotated 90° counterclockwise around the origin:

$(x,y)$ → $(-y,x)$

2. Then, as you can see, you must switch $x$ and $y$ and multiply $y$ by -1.

3. Keeping this on mind, you have that the vertices of the triangle A'B'C' are the following:

A(-2,-3)→A'(3,-2)

B(-5,-3)→B'(3,-5)

C(-4,-2)→C(2,-4)

4. Therefore, you can conclude that the answer is the option B.

You might be interested in

Round the following numbers to the nearest tenth 26.425

k0ka [10]

26.4 because .42 you have to leave the 4 the same since the 2 is not greater than 5.

8 0

3 years ago

3. A person standing 3 feet away from the base of a lamp post casts a shadow 4 feet long. If the person is 6 feet tall and walks

german

Answer:

533.33 ft/min

Step-by-step explanation:

We are given that

x=3 feet

y=4 feet

Height of person,h=6 feet

$\frac{dx}{dt}=400 ft/min$

Triangle ABC and A'B'C are similar because all right triangles are similar

By using similarity property

$\frac{h'}{6}=\frac{7}{4}$

$h'=10.5 feet$

$x+y=3+4=7 feet$

$\frac{h'}{6}=\frac{x+y}{y}$

$\frac{10.5}{6}=\frac{x+y}{y}$

$10.5y=6x+6y$

$10.5y-6y=6x$

$4.5y=6x$

Differentiate w.r.t t

$4.5\frac{dy}{dt}=6\frac{dx}{dt}$

$\frac{dy}{dt}=\frac{6\times 400}{4.5}ft/min$

$\frac{dy}{dt}=533.33ft/min$

Hence, If the person is 6 feet tall and walks away from the lamp post at a speed of 400 feet per minute then his shadow moving at the rate 533.33 ft/min

7 0

2 years ago

Can you please help me with this side of these problems.

Vlad [161]

Answer:

6: Reason 2 - substitution, Statement 4 - PR congruent to PR, Reason 4 - reflexive property, Reason 5 - AAS

8: Rotation

Step-by-step explanation:

6: Since both of the given angles equal 90°, you can substitute Angle RPT in to make Angle PRQ congruent to Angle RPT. Then, since both triangles share Line PR, PR would be congruent to PR by the reflexive property. And since you know that Angle Q is congruent to Angle T, you can see that Triangle QRP is congruent to Triangle TPR by the AAS theorem.

8: Since the 1st triangle is pointing to the right and the 2nd triangle is pointing downward, this would be a rotation of 90° clockwise (or 90° counterclockwise if the 1st triangle is the one pointing downward)

I don't have 7, sorry.

Also (if you haven't noticed it already), there's a typo in the 1st statement of the proof. Just thought I'd let you know ;)

5 0

2 years ago

In triangle ABC the length of side a AB is 10 inches and a length of side BC is 17 inches which of the following could be the le

Goryan [66]

Answer:

AC=16 inches

Step-by-step explanation:

Given two side lengths of a triangle as x and y (x greater than y), the third side z must satisfy the inequality:

x - y ≤ z ≤ x + y

The side lengths are x=17 and y=10, thus:

17 - 10 ≤ z ≤ 17 + 10

7 ≤ z ≤ 27

The third side must be between 7 and 27 inches. The only choice that satisfies the conditions is AC=16 inches

7 0

3 years ago

Evaluate g(r)=-5r+13 g(3)

RideAnS [48]

Answer:

r57

Step-by-step explanation:

6 0

3 years ago