Transcript: Homework Zone: Math - Translations on a Grid
Charmaine and Shahana stand in a classroom next to a big touch screen showing a coordinate grid with two triangles. They are in their twenties. Charmaine has black hair in a ponytail and Shahana has shoulder-length brown hair. They wear blue T-shirts with a print that reads "Home Work Zone."
Charmaine says HI,
TVO KIDS.
I'M TEACHER
CHARMAINE.
Shahana says AND I'M
TEACHER SHAHANA,
AND WE'RE HERE TO
SHOW YOU HOW
TO PERFORM
ONE TYPE OF
TRANSFORMATION,
CALLED A
TRANSLATION.
Charmaine says YOU CAN ALSO
THINK OF
A TRANSLATION
AS SLIDING AN
IMAGE ACROSS A
COORDINATE GRID.
Shahana says LET'S GIVE IT
A TRY WITH THIS
TRIANGLE THAT WE
HAVE OVER HERE.
LET'S NAME IT
TRIANGLE ABC.
NOW THE FIRST
THING WE NEED
TO DO IS IDENTIFY
THE POINTS
ON THE
SHAPE BEFORE
WE CAN MOVE IT
ANYWHERE.
SO I'D SAY
THAT POINT A
LOOKS LIKE IT
IS AT ONE
ON THE
X-AXIS,
AND ONE ON THE
Y-AXIS.
SO I WOULD
SAY THAT IT'S
COORDINATE PAIR
IS (1,1).
Using a marker, Charmaine writes down the values mentioned.
Charmaine says TO ME, IT
LOOKS LIKE
POINT B IS AT,
ON THE X-AXIS,
IT'S AT FIVE
AND ON
THE Y-AXIS,
IT'S ON ONE.
SO THE COORDINATES
WOULD BE (5,1).
Shahana says AND FINALLY,
POINT C LOOKS LIKE
IT'S THREE ACROSS
ON THE X-AXIS
AND FOUR UP
ON THE Y-AXIS,
SO C IS LOCATED
AT (3,4)
ON
OUR GRID.
ALRIGHT,
TIME TO MOVE
WHAT WE CALL
OUR FIGURE.
SO WE'RE
GOING TO NAME
THIS ORIGINAL
TRIANGLE ABC,
OUR ORIGINAL
FIGURE.
SUPPOSE THAT
WE WANT TO MOVE
OUR TRIANGLE, OR
TRANSLATE IT,
THREE TO THE
RIGHT, AND FOUR UP.
Charmaine says SO LET'S START
WITH
POINT
A AGAIN,
AND WE'RE GOING
TO MOVE IT
THREE TO
THE RIGHT.
ONE, TWO,
THREE,
AND THEN
FOUR UP.
ONE, TWO,
THREE, FOUR.
HERE'S OUR NEW
POINT.
SO WE WOULD
CALL THAT A PRIME,
AND THE NEW
COORDINATES
WOULD
BE...
Shahana says LOOKS LIKE
IT'S AT (4,5).
YOU'RE GOING
TO DO THE
SAME THING
WITH POINT B.
MOVE IT
ONE, TWO, THREE
TO THE RIGHT,
AND ONE, TWO,
THREE, FOUR UP,
SO THAT OUR POINT
B PRIME
IS LOCATED
AT (8,5).
Charmaine says AND FOR
POINT C,
IF WE MOVE IT THREE
TO THE RIGHT -
ONE,
TWO THREE,
IT'S NOW
AT SIX,
AND IF WE
MOVE IT FOUR UP -
ONE, TWO, THREE,
FOUR,
IT'S
AT EIGHT.
SO POINT C PRIME
WOULD BE (6,8).
Shahana says PERFECT.
OKAY,
TIME TO CONNECT
THE DOTS.
SO WE
TAKE EACH OF
OUR NEW
POINTS,
AND WE'RE
GOING TO CREATE
OUR TRANSLATED
SHAPE.
NOW WE HAVE
TO CHECK TO SEE
WHETHER WE'VE
PERFORMED THE
TRANSLATION
CORRECTLY.
THERE ARE A
NUMBER OF WAYS
THAT WE CAN
DO THIS.
FIRST
THING YOU CAN
DO IS TAKE ANOTHER
TRIANGLE
THAT MAYBE
YOU CUT OUT FROM
A DIFFERENT PIECE
OF PAPER
OR YOU
DRAW IT ONTO
A TRANSPARENCY.
YOU'RE GOING
TO TRACE IT
SO THAT
IT MATCHES
THE ORIGINAL
FIGURE.
IF...
YOU MOVE YOUR
ENTIRE SHAPE
THREE TO THE
RIGHT AND FOUR UP,
IT SHOULD LAND
EXACTLY WHERE
YOU PLOTTED
YOUR POINTS
OR DIRECTLY
ON TOP,
WHAT WE
WOULD SAY IS
A CONGRUENT
TRIANGLE,
OR THE
SAME SHAPE.
Charmaine follows the steps Shahana explains.
She continues REMEMBER,
WHENEVER
YOU'RE
DESCRIBING
A TRANSLATION,
REMEMBER TO INCLUDE
THE NUMBER
OF UNITS
THAT YOU'RE
MOVING AND THE
DIRECTION
THAT
YOU'RE MOVING
IN, WHETHER
IT'S UP,
DOWN,
LEFT OR RIGHT.
AND FINALLY,
OUR TRANSLATED
SHAPE...
WE WOULD
CALL OUR IMAGE.
I'M TEACHER
SHAHANA...
Charmaine says AND I'M
TEACHER CHARMAINE.
Charmaine says HI,
TVO KIDS.
I'M TEACHER
CHARMAINE.
Shahana says AND I'M
TEACHER SHAHANA,
AND WE'RE HERE TO
SHOW YOU HOW
TO PERFORM
ONE TYPE OF
TRANSFORMATION,
CALLED A
TRANSLATION.
Charmaine says YOU CAN ALSO
THINK OF
A TRANSLATION
AS SLIDING AN
IMAGE ACROSS A
COORDINATE GRID.
Shahana says LET'S GIVE IT
A TRY WITH THIS
TRIANGLE THAT WE
HAVE OVER HERE.
LET'S NAME IT
TRIANGLE ABC.
NOW THE FIRST
THING WE NEED
TO DO IS IDENTIFY
THE POINTS
ON THE
SHAPE BEFORE
WE CAN MOVE IT
ANYWHERE.
SO I'D SAY
THAT POINT A
LOOKS LIKE IT
IS AT ONE
ON THE
X-AXIS,
AND ONE ON THE
Y-AXIS.
SO I WOULD
SAY THAT IT'S
COORDINATE PAIR
IS (1,1).
Using a marker, Charmaine writes down the values mentioned.
Charmaine says TO ME, IT
LOOKS LIKE
POINT B IS AT,
ON THE X-AXIS,
IT'S AT FIVE
AND ON
THE Y-AXIS,
IT'S ON ONE.
SO THE COORDINATES
WOULD BE (5,1).
Shahana says AND FINALLY,
POINT C LOOKS LIKE
IT'S THREE ACROSS
ON THE X-AXIS
AND FOUR UP
ON THE Y-AXIS,
SO C IS LOCATED
AT (3,4)
ON
OUR GRID.
ALRIGHT,
TIME TO MOVE
WHAT WE CALL
OUR FIGURE.
SO WE'RE
GOING TO NAME
THIS ORIGINAL
TRIANGLE ABC,
OUR ORIGINAL
FIGURE.
SUPPOSE THAT
WE WANT TO MOVE
OUR TRIANGLE, OR
TRANSLATE IT,
THREE TO THE
RIGHT, AND FOUR UP.
Charmaine says SO LET'S START
WITH
POINT
A AGAIN,
AND WE'RE GOING
TO MOVE IT
THREE TO
THE RIGHT.
ONE, TWO,
THREE,
AND THEN
FOUR UP.
ONE, TWO,
THREE, FOUR.
HERE'S OUR NEW
POINT.
SO WE WOULD
CALL THAT A PRIME,
AND THE NEW
COORDINATES
WOULD
BE...
Shahana says LOOKS LIKE
IT'S AT (4,5).
YOU'RE GOING
TO DO THE
SAME THING
WITH POINT B.
MOVE IT
ONE, TWO, THREE
TO THE RIGHT,
AND ONE, TWO,
THREE, FOUR UP,
SO THAT OUR POINT
B PRIME
IS LOCATED
AT (8,5).
Charmaine says AND FOR
POINT C,
IF WE MOVE IT THREE
TO THE RIGHT -
ONE,
TWO THREE,
IT'S NOW
AT SIX,
AND IF WE
MOVE IT FOUR UP -
ONE, TWO, THREE,
FOUR,
IT'S
AT EIGHT.
SO POINT C PRIME
WOULD BE (6,8).
Shahana says PERFECT.
OKAY,
TIME TO CONNECT
THE DOTS.
SO WE
TAKE EACH OF
OUR NEW
POINTS,
AND WE'RE
GOING TO CREATE
OUR TRANSLATED
SHAPE.
NOW WE HAVE
TO CHECK TO SEE
WHETHER WE'VE
PERFORMED THE
TRANSLATION
CORRECTLY.
THERE ARE A
NUMBER OF WAYS
THAT WE CAN
DO THIS.
FIRST
THING YOU CAN
DO IS TAKE ANOTHER
TRIANGLE
THAT MAYBE
YOU CUT OUT FROM
A DIFFERENT PIECE
OF PAPER
OR YOU
DRAW IT ONTO
A TRANSPARENCY.
YOU'RE GOING
TO TRACE IT
SO THAT
IT MATCHES
THE ORIGINAL
FIGURE.
IF...
YOU MOVE YOUR
ENTIRE SHAPE
THREE TO THE
RIGHT AND FOUR UP,
IT SHOULD LAND
EXACTLY WHERE
YOU PLOTTED
YOUR POINTS
OR DIRECTLY
ON TOP,
WHAT WE
WOULD SAY IS
A CONGRUENT
TRIANGLE,
OR THE
SAME SHAPE.
Charmaine follows the steps Shahana explains.
She continues REMEMBER,
WHENEVER
YOU'RE
DESCRIBING
A TRANSLATION,
REMEMBER TO INCLUDE
THE NUMBER
OF UNITS
THAT YOU'RE
MOVING AND THE
DIRECTION
THAT
YOU'RE MOVING
IN, WHETHER
IT'S UP,
DOWN,
LEFT OR RIGHT.
AND FINALLY,
OUR TRANSLATED
SHAPE...
WE WOULD
CALL OUR IMAGE.
I'M TEACHER
SHAHANA...
Charmaine says AND I'M
TEACHER CHARMAINE.
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