The coordinatesof the imageof any point will be the point. The translationcan be
representedas a matrixsum.
Example 4
Whatis the imageof point in this translation?The secondrow representspoint. The imageof is.Notice:- The rowsof the secondmatrixare all the same.This is becauseeachpointof the triangle,or any point,
movesthe samedistanceand directionin this translation. - If the translationhad movedeachpoint unitsto the left and unitsup, then the secondmatrixin the
sum wouldhavebeen:LessonSummary
A matrixis an arrangementof numbersin rowsand columns.Matriceshavetheir own brandof arithmetic.
So far you havelearnedhow to add two matrices.
Matriceshavemanyapplications,for examplein businessand industry. One use of matricesis in working
with transformationsof pointsand figuresin a coordinateplane.In this lessonyou saw that additionof ma-
tricescan representa translation.An unusualfeatureof a translationmatrixis that all the rows are the same.
Pointsto Consider
In upcominglessonswe’ll learnabouttwo kindsof multiplicationwith matrices.We’ll then use multiplication
of matricesto representothertypesof transformationsin the coordinateplane,startingwith reflectionsin
the next lesson.
Somethingyou rely on all the time,but probablydon'tthinkaboutvery muchis the fact that any two real
numberscan be addedand multipliedand the resultis also a real number. Matricesare differentfrom real
numbersbecausethereare specialconditionsfor addingand multiplyingmatrices.For example,not all
matricescan be addedbecausein orderto add two matricesthe addendsmusthavethe samedimensions.
The conditionson matrixmultiplicationare evenmoreinteresting,as you shall see shortly.
LessonExercises
Fill in the blanks.