+0

# Help!

+1
118
5
+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?

$$\frac13 + \frac{n}7 < 1$$

Apr 17, 2021

#1
+121004
+3

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)

Apr 17, 2021
#2
+2124
+2

looks like cphill has alr answered 1 and 2. :))

3.

(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. :)))

=^._.^=

Apr 17, 2021
#4
+121004
+1

THX, catmg   !!!!

CPhill  Apr 17, 2021
#3
+50
+1

Thank you so much! (CPhill too!)

Apr 17, 2021
#5
+2124
0

You're welcome. :))

=^._.^=

catmg  Apr 17, 2021