- WELCOME TO A LESSON ON POINTS AND ORDERED PAIRS.
THE GOALS OF THIS VIDEO ARE TO PLOT POINTS
IN THE COORDINATE PLANE
AND ALSO TO DETERMINE THE COORDINATES OF POINTS
ON THE COORDINATE PLANE.
TO GRAPH OR PLOT POINTS WE USE TWO PERPENDICULAR NUMBER LINES
CALLED AXES.
THE HORIZONTAL NUMBER LINE IS CALLED THE X-AXIS,
AND WE HAVE THE POSITIVE X VALUES ON THE RIGHT
AND THE NEGATIVE X VALUES ON THE LEFT.
AND THE VERTICAL NUMBER LINE IS CALLED THE Y-AXIS,
AND THE POSITIVE Y VALUES ABOVE THE X-AXIS,
AND THE NEGATIVE Y VALUES ARE BELOW THE X-AXIS.
THE POINT AT WHICH THE AXES CROSS IS CALLED THE ORIGIN,
HERE, AND EVERY POINT ON THE COORDINATE PLANE IS IDENTIFIED
BY WHAT'S CALLED AN ORDERED PAIR.
EVERY ORDERED PAIR CONSISTS OF AN X COORDINATE
AND A Y COORDINATE.
AND THE X COORDINATE TELLS WHETHER TO GO LEFT OR RIGHT
ON THE COORDINATE PLANE,
AND THE Y COORDINATE TELLS YOU WHETHER TO GO UP OR DOWN
ON THE COORDINATE PLANE.
SO LET'S CONSIDER THE ORDERED PAIR (4, 3).
AS WE JUST STATED THE FIRST COORDINATE IS THE X COORDINATE,
AND THE SECOND COORDINATE IS THE Y COORDINATE.
SO TO PLOT THE POINT (4, 3) ON THE COORDINATE PLANE
WE START AT THE ORIGIN,
AND WE MOVE HORIZONTALLY TO THE RIGHT FOUR UNITS
SINCE THE X COORDINATE IS +4.
THEN WE MOVE VERTICALLY UP THREE UNITS
BECAUSE THE Y COORDINATE IS +3, AND THEN WE MAKE A POINT.
THIS IS THE POINT (4, 3).
LET'S GO AHEAD AND TRY A FEW MORE OF THESE.
WE WANT TO PLOT THE FOLLOWING POINTS.
AND AGAIN, I THINK IT'S HELPFUL TO THINK THAT THE X COORDINATE
TELLS YOU WHETHER TO GO LEFT OR RIGHT,
AND THE Y COORDINATE TELLS YOU WHETHER YOU NEED TO GO UP
OR DOWN BASED UPON THE SIGN.
SO FOR THE POINT A--
AND WE USUALLY IDENTIFY POINTS BY CAPITAL LETTERS.
SO FOR POINT A, WHICH HAS COORDINATES (-3, 2),
SINCE THE X COORDINATE IS NEGATIVE 3,
WE START AT THE ORIGIN AND GO LEFT THREE UNITS THIS TIME,
AND THEN UP TWO UNITS BECAUSE THE Y COORDINATE IS +2,
AND WE MAKE A POINT.
THIS WOULD BE POINT A.
THE NEXT POINT, POINT B HAS AN X COORDINATE OF -1
SO WE GO LEFT ONE,
AND THEN THE Y COORDINATE IS +4 SO WE GO UP FOUR UNITS.
SO LEFT ONE UNIT, UP FOUR UNITS TO POINT B.
POINT C, X COORDINATE IS -2 SO WE GO LEFT TWO UNITS,
AND THE Y COORDINATE IS -4 NOW
SO WE GO DOWN FOUR UNITS TO POINT C.
D HAS THE COORDINATES (0, -2).
THIS ZERO TELLS US WE DO NOT GO LEFT OR RIGHT AT ALL.
WE STAY RIGHT AT THE ORIGIN,
BUT WITH THE Y COORDINATE OF -2 WE NEED TO GO DOWN TWO UNITS.
AND LASTLY, THE POINT (3,0).
THIS 3 TELLS US TO GO RIGHT THREE UNITS,
AND THE Y COORDINATE OF ZERO TELLS US THAT
WE DO NOT GO UP OR DOWN. WE STAY RIGHT ON THE X-AXIS.
SO THE POINT (3, 0) WOULD BE RIGHT HERE ON THE X-AXIS.
LET'S GO AHEAD AND TRY THIS IN THE OPPOSITE DIRECTION NOW.
WE'RE GIVEN SEVERAL POINTS THAT ARE PLOTTED
AND WE WANT TO IDENTIFY THE COORDINATES.
WELL THE EASIEST WAY TO DO THIS IS JUST DRAW A LINE
STRAIGHT TO THE X-AXIS AND STRAIGHT TO THE Y-AXIS.
AS WE CAN SEE THE X COORDINATE IS +1
AND THE Y COORDINATE IS +5.
SO A HAS THE ORDERED PAIR (1, 5).
WE DO NEED TO BE CAREFUL THAT WE LIST THE X COORDINATE FIRST.
SO FOR POINT B THE X COORDINATE WOULD BE -6,
AND THE Y COORDINATE +2.
POINT C, THE X COORDINATE IS -2, AND THE Y COORDINATE IS -4.
D, THE X-COORDINATE +4, Y COORDINATE -4.
NOTICE E IS RIGHT ON THE Y-AXIS.
AGAIN, WE FOLLOW THE SAME RULES.
DRAW A SEGMENT STRAIGHT TO THE X-AXIS, WHICH WOULD BE ZERO.
AND THE POINT IS ON THE Y-AXIS RIGHT AT -2.
SO THE COORDINATES WOULD BE (0, -2).
AND LASTLY, POINT F, THE X COORDINATE WOULD BE 7,
AND THE Y COORDINATE WOULD BE ZERO.
NOW WE CAN CHECK OUR WORK ON THE GRAPHING CALCULATOR
BECAUSE THE GRAPHING CALCULATOR WILL PLOT POINTS.
SO WHAT WE'RE GOING TO DO IS GO AHEAD AND ENTER THESE POINTS
IN THE CALCULATOR AND SEE IF IT MATCHES OUR GRAPH.
THE WAY WE ENTER IN POINTS TO BE PLOTTED
IS WE HIT THE STAT KEY, ENTER.
THEN WE'LL ENTER IN ALL OF THE X COORDINATES IN L1
AND ALL OF THE Y COORDINATES IN L2.
AND THIS WORKS JUST LIKE EXCEL
SO WHEN YOU HIT ENTER IT DROPS DOWN TO THE NEXT CELL.
NOW WE ENTER ALL THE Y COORDINATES.
NEXT WE WILL PRESS SECOND Y EQUALS,
AND WE NEED TO TURN ON THE STAT PLUS SO WE PRESS ENTER.
WHEN IT'S BLINKING ON ON WE HIT ENTER.
THIS FIRST OPTION HERE IS TO PLOT POINTS,
WHICH IS WHAT WE WANT. WE HAVE OUR X COORDINATES IN L1.
WE HAVE OUR Y COORDINATES IN L2,
AND WE CAN SELECT THE TYPE OF POINT WE'D LIKE TO PLOT.
I'LL GO AHEAD AND LEAVE IT ON THIS FIRST OPTION.
NOW TO MAKE IT LOOK EXACTLY LIKE THIS ONE
WE SHOULD CHOOSE THE SAME WINDOW.
SO IF WE PRESS WINDOW AND CHANGE THE X MIN TO -8
AND THE X MAX TO +8,
AND THE Y VALUES START AT -6 AND GO UP TO +6.
NOW WE CAN PRESS GRAPH,
AND WE CAN SEE THAT THIS GRAPH DOES MATCH THE GRAPH
THAT WE SEE ON THIS SLIDE.
SO THAT'S A NICE WAY TO CHECK YOUR WORK
IF YOU HAVE A GRAPHING CALCULATOR.
I HOPE YOU FOUND THIS VIDEO HELPFUL.
THANK YOU AND HAVE A NICE DAY.