Find the slope of a line perpendicular to a line through the given points.. . E(5, 7), F(3 , 1)

2 answers:

6 0

Slope of perpendicular lines multiply to -1

find slope of this line

slope=(y2-y1)/(x2-x1)
(x,y)
(5,7)
(3,1)
slope=(1-7)/(3-5)=-6/-2=6/2=3

perpendular lines have slopes taht mutliply to -1
3 times what=-1
-1/3

slope of perpendiular is -1/3

Firdavs [7]3 years ago

6 0

Answer:

slope of perpendiular is -1/3

Step-by-step explanation:

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The point below will be reflected over the line y = x and then translated two units left and one unit up.5421-5-4-3-2-10234-1-2-

charle [14.2K]

A reflection over the line y=x implies exchanging the x and y coordinates of a point. For example if you take a generic point (a,b) then its reflection over y=x is (b,a). Our point is (-1,3) so its reflection over y=x is the point (3,-1).

Then we have to translate it two units left. Translating a point left means that we are moving towards negative x values so we need to substract 2 from the x coordinate:

$(3,-1)\rightarrow(3-2,-1)=(1,-1)$

Finally we have to translate it 1 unit up towards positive y values so we have to add 1 to its y coordinate:

$(1,-1)\rightarrow(1,-1+1)=(1,0)$

And these are the final coordinates. In the following picture you have the points you get after each step (from A to D) with the y=x line in blue:

4 0

1 year ago

The water level in a lake was monitored and was noted to have changed -2 1/3 inches in one year. The next year it was noted to h

Diano4ka-milaya [45]

Answer:

The total change in water level over the past 2 years is $\displaystyle -4 \frac{1}{6}$ .

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Fractions

Proper and Improper

Numbers

Least Common Multiple (LCM)

Step-by-step explanation:

Step 1: Define

Identify

Year 1 water change: $\displaystyle -2 \frac{1}{3}$

Year 2 water change: $\displaystyle -1 \frac{5}{6}$

Step 2: Find Total Water Change

[Set up] Add yearly water changes: $\displaystyle -2 \frac{1}{3} + -1 \frac{5}{6}$
[Fractions] Convert to improper: $\displaystyle \frac{-7}{3} - \frac{11}{6}$
[Fraction] Rewrite [LCM]: $\displaystyle \frac{-14}{6} - \frac{11}{6}$
[Order of Operations] Subtract: $\displaystyle \frac{-25}{6}$
[Fraction] Convert to proper: $\displaystyle -4 \frac{1}{6}$