+50 1-What is the distance on a Cartesian coordinate plane from (1,-1) to (7,7)
2- The midpoint of the line segment between (x,y) and (2,4) is (-7,0). Find (x,y).
3-The equation of the line that passes through the points (-3,5) and (0,-4) can be expressed in the form y=mx+b. What is the value of m+b?
4-What is the slope of a line perpendicular to the line containing the points (4,-7) and (-5,-1)? Express your answer as a common fraction.
5- What is the largest whole number value of that makes the following inequality true?
\(\frac13 + \frac{n}7 < 1\)
+128474 1. Distance Formula
sqrt [ ( 7 - 1)^2 + ( - 1 - 7)^2 ] = sqrt [ 6^2 + (-8)^2 ] = sqrt [ 36 + 64] = sqrt 100 = 10
2.
Midpoint = [ ( x + 2) /2 , (y + 4) /2 ]
( -7,0) = [ (x+ 2)/2 , ( y + 4) / 2)
Equating things we have that
(x + 2) / 2 = -7 (y + 4) / 2 = 0
x + 2 = -7*2 y + 4 = 2*0
x + 2 = - 14 y + 4 = 0
x = -14 - 2 = -16 y = -4
(x, y) = ( -16. -4)
+2401 looks like cphill has alr answered 1 and 2. :))
3.
You want to start with finding the slope, "m".
(5--4)/(-3-0) = 9/-3 = -3.
Then we can pllug one of the points in.
y = -3x+b
5 = -3(-3) + b
b = -4
y = -3x-4
4.
For this one, we just need the slope.
(-7--1)/(4--5) = -6/9 = -2/3
A perpendicular slope is oposite.
Take the negative and recipical. 3/2
5.
1/3 + n/7 < 1
n/7 < 2/3
n < 14/3
n = 4
I hope this helped. :)))
=^._.^=
