Let C be between point D and E.

Pls, help me with this math question

olya-2409 [2.1K]

Answer:

Perimeter $\sqrt{26}+\sqrt{5}+\sqrt{10}+\sqrt{17}$ units. Area 12 square units.

Step-by-step explanation:

Perimeter: total distance around the figure.

Distance Formula: the distance between points $\left(x_1,y_1\right) \text{ and } \left(x_2,y_2\right)$ is

$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$AB=\sqrt{(6-1)^2+(2-1)^2}=\sqrt{25+1}=\sqrt{26}$

$BC=\sqrt{(5-6)^2+(4-2)^2}=\sqrt{1+4}=\sqrt{5}$ $CD=\sqrt{(2-5)^2+(5-4)^2}=\sqrt{9+1}=\sqrt{10}$ $DA=\sqrt{(1-2)^2+(1-5)^2}=\sqrt{1+16}=\sqrt{17}$

The perimeter is the sum of all those segment lengths.

One way to find the area of the figure is to surround it with a rectangle, insert some lines so that the areas you do not want can be found and subtracted from the rectangle's area. (See attached image.)

The area of the large rectangle around the figure is 5 x 4 = 20 square units.

The triangles have areas 1/2 (base) (height):

A. (1/2)(1)(4) = 2 square units

B. (1/2)(3)(1) = 1.5 square units

D. (1/2)(1)(2) = 1 square unit

E. (1/2)(5)(1) = 2.5 square units

Square C. (1)(1) = 1 square unit

Total of all the area you don't want to include:

2 + 1.5 + 1 + 2.5 + 1 = 8 square units

Subtract 8 from the surrounding rectangle's area of 20, and you get the area of the figure is 20 - 8 = 12 square units.

4 0

3 years ago

What is the equation of the line that is perpendicular to y= -3x + 1 and passes through (2,3)?

Aleonysh [2.5K]

Answer:

$\large\boxed{y=\dfrac{1}{3}x+2\dfrac{1}{3}}$

Step-by-step explanation:

$\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=-3x+1\to m_1=-3.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-3}=\dfrac{1}{3}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{3}x+b.\\\\\text{The line passes through }(2,\ 3).$

$\text{Put the coordinates of the point to the equation.}\ x=2,\ y=3:\\\\3=\dfrac{1}{3}(2)+b\\\\3=\dfrac{2}{3}+b\qquad\text{subtract}\ \dfrac{2}{3}\ \text{from both sides}\\\\b=2\dfrac{1}{3}$

3 0

3 years ago

Read 2 more answers

Easy math please help

insens350 [35]

1) False

Adjacent angles must share a common side/ray.

2) B and D

Adjacent angles are those that are directly next to each other and share a common side.

3) C

Angles 1 and 2 are congruent. Angles 3 and 4 are congruent. Both of these pairs have angles that are opposite each other.

4) B

Angles 1 and 2 add up to 180. Angles 3 and 4 add up to 180. Both of these pairs of angles are supplementary.

5) A

These angles are directly next to each other and share a common side.

Hope this helps!! :)

4 0

2 years ago

HELPPP PLSSS 18. A triangle has verticesA(4,3), B(6,9) and C(2, -3). The triangle is rotated 90°

Mariulka [41]

Answer:

F and H are NOT true

Step-by-step explanation:

Rotation 90° CCW is represented by the transformation ...

(x, y) ⇒ (-y, x)

Then the rotated coordinates are ...

A(4, 3) ⇒ A'(-3, 4) . . . . . quadrant II

B(6, 9) ⇒ B'(-9, 6) . . . . . quadrant II

C(2, -3) ⇒ C'(3, 2) . . . . . quadrant I

The rotated figure will be congruent to the original, because rotation is a rigid transformation.

__

Consider the answer choices:

F: (-3, -4) is A' --- NOT true

G: triangles are congruent --- true

H: B is in quadrant III --- NOT true

J: (3, 2) is the coordinates of C' --- true

Both choices F and H are NOT true.

8 0

2 years ago

5) Which one of the following proportions is NOT true?*

Tpy6a [65]

The second one, 69/24 = 23/8 and cannot be simplified further

6 0

3 years ago