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The Distance Formula?

The coordinates of 3 bus stops on a map are A(-8,0) B(-6,2) and C(-2,6). What is the ratio of the length of BC to the length of AC?

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PIYUSH L. | Maths tutoring for middle school to college maths studentsMaths tutoring for middle school to coll...
5.0 5.0 (6 lesson ratings) (6)
Hi Dalyia,
Distance between two points A(x1,y1) and B(x2,y2) is given by √((y2-y1)^2+(x2-x1)^2)

BC = √(6-2)^2+(-2+6)^2 = 4√2

AC = √(6-0)^2+(-2+8)^2=6√2

Therefore BC/AC = 2/3
Have a good day !!!
Shannon P. | Specialized, flexible tutoring in Math, Language Arts, and FrenchSpecialized, flexible tutoring in Math, ...
4.9 4.9 (92 lesson ratings) (92)
Good morning, Dalyia!

The first thing you should do is mark these three points on a graph, just so you have a visual of what you're working on. After you've plotted the points, draw a line from C to (-2,0), then a line from (-2,2) to B. Notice you have two right triangles now.

Now, let's work on the smaller triangle first. If you count the units for the sides of the triangle not including the hypotenuse, you'll see the vertical side is 4 units, and the horizontal side is 4 units, as well. Knowing that, we can use the Pythagorean Theorem to find side BC (a^2+b^2=c^2). So, if we plug in our sides, we have 4^2+4^2=c^2 => 32=c^2 => c=6. Line BC is 6.

The same can be done for line AC. The sides of that triangle are 6 units each, so: 6^2+6^2=c^2 => 72=c^2 => c=8.49. Thus, side AC is 8.49.

All you have to do now is set up the ratio as asked, which is the lengths of side BC to AC, which makes 6:8.49, or 6/8.49.
Hope this helps!


Hi Dalyia,
The square root of 32 is 5.66 not 6.  Therefore, line BC is 5.66.
The ratio of BC to AC will be 2/3 as determined from Piyush's answer.
Apparently, I had not had enough coffee this morning.  I apologize for my mistakes and any confusion!  Disregard my input.