When the endpoints of a line segment are known, we can find the point midway between them. This point is known as the midpoint and the formula is known as the
midpoint formula . Given the endpoints of a line segment,
and
the midpoint formula states how to find the coordinates of the midpoint
A graphical view of a midpoint is shown in
[link] . Notice that the line segments on either side of the midpoint are congruent.
Finding the midpoint of the line segment
Find the midpoint of the line segment with the endpoints
and
Use the formula to find the midpoint of the line segment.
We can locate, or plot, points in the Cartesian coordinate system using ordered pairs, which are defined as displacement from the
x- axis and displacement from the
y- axis. See
[link] .
An equation can be graphed in the plane by creating a table of values and plotting points. See
[link].
Using a graphing calculator or a computer program makes graphing equations faster and more accurate. Equations usually have to be entered in the form
y= _____. See
[link].
Finding the
x- and
y- intercepts can define the graph of a line. These are the points where the graph crosses the axes. See
[link] .
The distance formula is derived from the Pythagorean Theorem and is used to find the length of a line segment. See
[link] and
[link] .
The midpoint formula provides a method of finding the coordinates of the midpoint dividing the sum of the
x -coordinates and the sum of the
y -coordinates of the endpoints by 2. See
[link] and
[link] .
Section exercises
Verbal
Is it possible for a point plotted in the Cartesian coordinate system to not lie in one of the four quadrants? Explain.
Answers may vary. Yes. It is possible for a point to be on the
x -axis or on the
y -axis and therefore is considered to NOT be in one of the quadrants.
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
