Question #ce20f
1 Answer
Draw a triangle diagram to be played around with, or in this case, simply average each coordiante to get
Explanation:
We'd like to know the steepness of the line so that we can visualize this geometrically without actually plotting points. Calculate the slope:
Ah, so it's a positive but low steepness. Here's a sketch of what a line between those two points should look like (as a right triangle, with the right angle on a point
Ultimately, line
From there, we can see that point
Yes, the picture does not exactly match the slope, but that's not the point. Here, what we're looking for is a point
So, what are the coordinates of point
Similarly, a horizontal line from point
This may seem useless, but this will help us find the coordinates of point
Since line
Finally, because the length of line
And since these two triangles are congruent, all of their sides and angles are equal!
So
Here, to solve for the coordinates of point
We already know the coordinates of point
Then to solve for
And then for
So the coordinates of point
... Wait, isn't that the same as averaging the coordinates of the two points (point
OK, sure it is, but that rule only applies if the point happens to be exactly in the middle. What I have demonstrated coould be used and slightly tweaked (using AAA instead of ASA, showing that the smaller triangles are similar, and using a proportionality constant before getting to the answer) in cases where it isn't.