Mathematics, 01.12.2020 03:00, kaleec

Find an equation for the perpendicular bisector of the line segment whose endpoints are (-1,5) and (-7, -7).

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answered: LaytonHall79

The equation of the perpendicular bisector is y = $\frac{-1}{2}$ x - 3

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

m is the slopeb is the y-intercept

The rule of the slope is m = $\frac{y2-y1}{x2-x1}$ , where

(x1, y1) and (x2, y2) are two points on the lineThe rule of the mid-point is M = ( $\frac{x1+x2}{2},\frac{y1+y2}{2}$ )The product of the slopes of the perpendicular lines is -1, that means if the slope of one is m, then the slope of the other is $\frac{-1}{m}$ (we reciprocal m and change its sign).

∵ A line passes through points (-1, 5) and (-7, -7)

∴ x1 = -1 ad y1 = 5

∴ x2 = -7 and y2 = -7

→ Use the rule of the slope above to find the slope of the line

∵ m = $\frac{-7-5}{-7--1}$ = $\frac{-12}{-7+1}$ = $\frac{-12}{-6}$ = 2

∴ m = 2

→ Reciprocal the value of m and change its sign to find the slope of

the line perpendicular line

∴ m⊥ = $\frac{-1}{2}$

→ Substitute in the form of the equation above

∵ y = $\frac{-1}{2}$ x + b

∵ The ⊥ line is also the bisector of the given line, find the mid-point

of the given line because it is also lying on the ⊥ line

∵ M = ( $\frac{-1+-7}{2},\frac{5+-7}{2}$ ) = ( $\frac{-8}{2},\frac{-2}{2}$ ) = (-4, -1)

∴ M = (-4, -1)

→ Substitute the coordinates of M in the equation of the ⊥ line above

∵ x = -4 and y = -1

∴ -1 = $\frac{-1}{2}$ (-4) + b

∴ -1 = 2 + b

→ Subtract 2 from both sides

∴ -3 = b

→ Substitute the value of b in the equation

∴ y = $\frac{-1}{2}$ x + -3

∴ y = $\frac{-1}{2}$ x - 3

∴ The equation of the perpendicular bisector is y = $\frac{-1}{2}$ x - 3

answered: Guest

the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. hope this ! mark brainliest! you v much! : )

answered: Guest

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number $c\in[0.5,0.75]$ that satisfies the conclusion of the mean value theorem, that is, a number $c\in[0.5,0.75]$ such that

$f'(c) = \dfrac{f(0.75) - f(0.5)}{0.75-0.5},$

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.