and
.
The questionasksyou to identifythe lengthof the segment.Becausethe segmentis not parallelto either
axis,it is difficultto measuregiventhe coordinategrid. However, it is possibleto thinkof this segmentas
the hypotenuseof a right triangle.Drawa verticalline at and a horizontalline at and find the
pointof intersection.This pointrepresentsthe third vertexin the right triangle.
You can easilycountthe lengthsof the legs of this triangleon the grid. The verticalleg extendsfromto , so it is unitslong.The horizontalleg extendsfrom to , so it is
unitslong.Use the PythagoreanTheoremwith thesevaluesfor the lengthsof eachleg
to find the lengthof the hypotenuse.
The segmentconnecting and is unitslong.Mathematicianshavesimplifiedthis processand createda formulathat uses thesestepsto find the distance
betweenany two pointsin the coordinateplane.If you use the distanceformula,you don’thaveto drawthe
extralines.