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The length of the segment between the points (2a, a-4) and (4, -1) is 2*sqrt10 units. What is the product of all possible values for a?

 Mar 20, 2020
 #1
avatar+12179 
+1

The length of the segment between the points (2a, a-4) and (4, -1) is 2*sqrt10 units. What is the product of all possible values for a?

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 Mar 20, 2020
 #2
avatar+23553 
+1

Use the distance formula      d^2 = (x1-x2)^2 + (y1-y2)^2

                                              d = sqrt ((x1-x2)^2 + (y1-y2)^2))

                                            2 sqrt10 = sqrt ((2a-4)^2 + (a-4 - - 1)^2

                                                           =  sqrt (4 a^2-16a+16+ a^2-6a+9)

                                                sqrt40    = sqrt(5 a^2 -22a +25)

                                                     40 = 5a^2-22a+25

                                                      0 = 5a^2-22a-15       from quadratic formula   a = 5   or -0.6      You can multiply them together....

 Mar 20, 2020

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