Devante is proving that perpendicular lines have slopes that are opposite reciprocals. he draws line m and labels two points on the line as (a, 0) and (0, b) . enter the answers, in simplest form, in the boxes to complete the proof. the slope of line m is . rotate line m 90° clockwise about the origin to get line n. the labeled points on line m map to (0, −a) and (, ) on line n. the slope of line n is . the slopes of the lines are opposite reciprocals because the product of the slopes is .

The slope of line m is (-b/a).

The labelled points on line m map to (0,-a) and (b,0) on the line n.

The slope of line n is (a/b).

The slopes of the lines are opposite reciprocals because the product of the slopes is -1.

Step-by-step explanation:

The slope of a line connecting the points (x₁,y₁) and (x₂,y₂) is

The slope of line m is

The line is rotated clockwise by an angle 90° to get line n.

The coordinates of the line n are (0,-a) and (b,0)

The slope of line n is

We see that,

m₁m₂ = -(b/a) * (a/b) = -1

Hence the products of the slopes of perpendicular lines is -1.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.