Find the distance between the points \((1,1)\) and \((4,7)\) . Express your answer in simplest radical form.
Draw it. You see that you can form a right triangle with the line between the two points is the hypotenuse.
The bottom leg is 4 – 1 = 3 units.
The right hand leg is 7 – 1 = 6 units.
Now all you have to do is use Pythagoras' Theorem.
32 + 62 = x2
so x2 = 45 and x (which is the hypotenuse) = 3 • sqrt(5) This is the distance between those two points.
You can use the distance formula:
It helps some people enormously when they understand that the distance formula IS JUST Pythagoras's theorem.
The distance in the y direction, y2-y1 IS the vertial rise. And x2-x1 IS the horizonal distance
If anyone wants me to explain better I can. Just ask.
Here's the explanation:
I couldn't find a picture, but the right angle corner is point C.
So, C's coordinates are \(\left(x_2,\:y_1\right)\)
BC is \(\left(y_2-y_1\right)\)
AC is \(\left(x_2-x_1\right)\)
I know you got the pic from somewhere and it is a good diagram. Give yourself a point
Later on, when you are able to draw such a pic yourself it would be better if there were actual number points on the diagram.
It makes it much easier for kids to understand what is going on.
I've just seen some of your other answers, I think I have underestimated your abilities. Sorry.
Maybe you can already produce a pic like this yourself.
If you do not already have the skill, try playing with GeoGebra.
Geogebra is a free program, it is what I use for most of my illustrative pics.
It took me a while to learn, and I am still learning, (just trial and error) but it is really fun to use.