Find an equation for the perpendicular bisector of the line segment whose endpoints
are (-1, -2) and (-5,4).

Step-by-step explanation:

Perpendicular Bisector

It's defined as a line that divides another line into two equal parts. The bisector passes through the midpoint of the line forming any angle, but if that angle is exactly 90°, then the bisector is also perpendicular.

We need to find the equation of the line that divides into equal parts the line with endpoints (-1, -2) and (-5,4) and is perpendicular to it.

First, let's find the slope of the line segment. The slope can be calculated with the formula:

The line for the perpendicular bisector has a slope m2. Two perpendicular lines with slopes m1 and m2 must comply:

Solving for m2:

The equation of the perpendicular bisector has the form:

Now we find the coordinates of the midpoint of the segment:

The midpoint is (-3,1). Using this point will allow us to find the value of b:

Thus, the equation for the perpendicular bisector is

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.