Using the Midpoint Formula Use Exercise 37 to find the points that divide the line segment joining the given points into four equal parts. (a) ( 1 , − 2 ) , ( 4 , − 1 ) (b) ( − 2 , − 3 ) , ( 0 , 0 )
Using the Midpoint Formula Use Exercise 37 to find the points that divide the line segment joining the given points into four equal parts. (a) ( 1 , − 2 ) , ( 4 , − 1 ) (b) ( − 2 , − 3 ) , ( 0 , 0 )
Midpoint of a line segment Show that the point with coordinates(x1 + x2 /2 , y1 + y2/2 )is the midpoint of the line segment joining P(x1 , y1) to Q(x2 , y2).
Angle Between Two Lines In Exercises 97 and 98,use the figure, which shows two lines whose equationsare y1 = m1x + b1 and y2 = m2x + b2. Assume thatboth lines have positive slopes. Derive a formula for theangle between the two lines. Then use your formula tofind the angle between the given pair of lines.
True or False? In Exercises 97–100, determine whetherthe statement is true or false. Justify your answer.97. To divide a line segment into 16 equal parts, you haveto use the Midpoint Formula 16 times.98. The points (−8, 4), (2, 11), and (−5, 1) represent thevertices of an isosceles triangle.99. The graph of a linear equation cannot be symmetricwith respect to the origin.100. A circle can have a total of zero, one, two, three, orfour x- and y-intercepts.101. Think About It When plotting points on therectangular coordinate system, when should you usedifferent scales for the x- and y-axes? Explain.
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