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2 years ago

Slope is written as a ratio of the vertical change (run) to the horizontal change (rise) between any two points on a line.

Mathematics

1 answer:

hichkok12 [17]2 years ago

6 0

Answer:

Step-by-step explanation:

Yeah the equation is change in y over change in x; change in is represented with the delta sign, so y2-y1/x2-x1

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How do I find the equation of the perpendicular bisector between (-2,5) and (2,-1)?

Arturiano [62]

Answer:

$y = \frac{2}{3} x + 2$

Step-by-step explanation:

Start by finding the slope of the given line.

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Slope of given line

$= \frac{5 - ( - 1)}{ - 2 - 2}$

$= \frac{5 + 1}{ - 4}$

$= \frac{6}{ - 4}$

$= - \frac{3}{2}$

A perpendicular bisector cuts through the line at its midpoint perpendicularly.

The product of the slopes of two perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

$- \frac{3}{2} m = - 1$

$m = - 1 \div ( - \frac{3}{2} )$

$m = - 1 \times ( - \frac{2}{3} )$

$m = \frac{2}{3}$

$y = \frac{2}{3}x + c$ , where c is the y-intercept.

To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

$\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}$

Midpoint of given line

$= ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )$

$=( \frac{0}{2} , \frac{4}{2} )$

= (0, 2)

$y = \frac{2}{3} x + c$

When x= 0, y= 2,

2= ⅔(0) +c

2= 0 +c

c= 2

Thus, the equation of the perpendicular bisector is $y = \frac{2}{3} x + 2$ .

7 0

2 years ago

Help please thanks :)

Galina-37 [17]

Answer:

270 anticlockwise

-90 clockwise

-450 clockwise

Step-by-step explanation:

The answer, going clockwise is -90. One leg of the angle is on the +x axis and the other is going down from the origin. The only other answer is 270 degrees. That angle is starting at the + x axis and goes anticlockwise. It has to travel to the dividing line between the 3rd and 4th quad.

-450 also works. Starting at 0 and going -360 clockwise leads you right back to the +x axis. -450 -(-360) leaves you with -90. Minus 90 degrees puts you on the line between the 3rd and 4th quadrant which is the same place 270 and - 90 will land.

Everything else takes you other places. 450 for example is the +y axis and that is related to 90 degrees not - 90.

3 0

2 years ago

May someone solve and give explanation

skelet666 [1.2K]

Answer:

θ = 49.4584°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Trigonometry

[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] cosθ = adjacent over hypotenuse
Inverse Trig

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = ?

Adjacent Leg = 13

Hypotenuse = 20

Step 2: Find Angle

Substitute in variables [cosine]: cosθ = 13/20
Inverse Trig: θ = cos⁻¹(13/20)
Evaluate: θ = 49.4584°

6 0

2 years ago

Determine if the representation below are proportional (p) or non-proportional (np)

Stolb23 [73]

The first one is not proportional and the second one is proportional.

7 0

2 years ago

PLEASE HELP ME .......!!

Kruka [31]

Answer:

wait is that a test if it is cheating

Step-by-step explanation:

well the first one go on the bottom 2 row secound one first row third first row but it is in happpy i am not reall good at math XD third last row forth very happy fifth on unhappy sixth very unhappy seven very unhappy eight on very happy i think i got it i did this before i just don't rembear but i tried

7 0

3 years ago