Question

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

Answer 1

This is almost purely an algebra question, but you need to remember the formula for the distance between two points as being:
\[d = \sqrt{(y _{2} - y_{1})^2 + (x_{2} - x_{1})^2 }\]
Substitute all the values in and you can get then square both sides, expanding brackets and rearrange the equation until you end up with a quadratic. Then, solve the quadratic to get your values of a.

Answer 2

Oh and in case you were wondering what a product is (a lot of people don't know!) it's just what you get when you multiply numbers together - so to get the product of your a values, you just multiply them together!

Answer 3

D=sqrt[ (y1-y2)^2+(x1-x2)^2]
D^2=(y1-y2)^2+(x1-x2)^2
(2*sqrt(10))^2=(-1-(a-4))^2+(4-2a)^2
40=(3-a)^2+(4-2a)^2
40=(9-6a+a^2)+(16-16a+4a^2)
40=25-22a+5a^2
5a^2-22a-15=0