PLEASE HELP! 1. Using the general points A and B, label and explain where the midpoint formula comes from.
A(x1,y1)
B(x2,y2)

2. Determine the midpoint of the following segments.
a) A (-4, 6) B (2,-3)

3. Demonstrate how the Pythagorean Theorem turns into the distance formula.
A(x1,y1)
B(x2,y2)

4. Determine the distance from A to B. Round your answer to the nearest tenth.
a) A (-4, 6) B (2,-3) b) A (2,-1) B (-10, 4)

Find the coordinates of the midpoint of the segment joining the given points.

5. (0, 2) and (6, 4)
6. (6, -7) and (-6, 3)

7. What coordinate point is the midpoint of the line segment that goes from point (-1,3) to point (5,-5) in the standard (x, y) coordinate plane?

A. (-3,4)
B. (2,-1)
C. (3,-1)
D. (2,4)

Find the distance between the two points.

8. (-4, 2) and (2, -1)

9. A triangular ramp from the ground to the bed of a truck that stands 6 feet off the ground has a base of 8 feet. How long in feet is the length of the ramp?
A. 5 feet
B. 5.29 feet
C. 8 feet
D. 10 feet
E. 100 feet

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

no this is a nonlinear negative