Respuesta :

sadafrahmanrakin

explanation:

The fastest way to find the missing endpoint is to determine the distance from the known endpoint to the midpoint and then performing the same transformation on the midpoint.  In this case, the x-coordinate moves from 4 to 2, or down by 2, so the new x-coordinate must be 2-2 = 0.  The y-coordinate moves from 4 to -5, or down by 9, so the new y-coordinate must be -5-9 = -14.

 

An alternate solution would be to substitute (4,4) for (x1,y1) and (2,-5) for (x,y) into the midpoint formula:

x=(x1+x2)/2

y=(y1+y2)/2

Solving each equation for (x2,y2) yields the solution (0,-14).

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Answer:

b = 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + y - 8 = 0 ( subtract 3x - 8 from both sides )

y = - 3x + 8 ← in slope- intercept form

with slope m = - 3

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]

Consider the second line with equation

- 2x + by + 9 = 0 ← rearrange into slop- intercept form

by = 2x - 9 ( divide terms by b ( b ≠ 0 )

y = [tex]\frac{2}{b}[/tex] x - [tex]\frac{9}{b}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{2}{b}[/tex]

Then

[tex]\frac{2}{b}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )

b = 6

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