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.
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
