# 21-223221083-College-Algebra77-converted.docx - 1.1 Sets of...

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1.1 Sets of Real Numbers and the Cartesian Coordinate Plane11ddpoints.) Our goal now is to create an algebraic formula to compute the distance between these two points. Consider the generic situation below on the left.Q (x1, y1)Q (x1, y1)P (x0, y0)P (x0, y0)(x1, y0)With a little more imagination, we can envision a right triangle whose hypotenusehas length d as drawn above on the right. From the latter figure, we see thatthe lengths of the legs of the triangle are |x1 x0| and |y1 y0| so thePythagoreanTheoremgives us|x1 x0| + |y1 y0| = d(x x )2+ (y y )2= d2(Do you remember why we can replace the absolute value notation withparentheses?) By extracting the square root of both sides of the second equationand using the fact that distance is never negative, we getEquation 1.1.The Distance Formula:The distance d between the points P (x0, y0) andQ (x1, y1) is:d=.(xx)2+(yy)2It is not always the case that the points P and Q lend themselves to constructingsuch a triangle. If the points P and Q