<p>p 860 Number 18 in blue book, i've looked at the solutions in teh consolidated list, but i still dont get it, can someone explain how slope can be used to calcute the sides of the triangle????</p>
<p>This is my first time trying to explain something, so if it's not clear, refer to the Consolidated Blue book answers lists!</p>
<p>Okay, basically, you use the slope to calculate points within 0<x<4 that COULD be on the line, since the hypotenuse of the triangle contains two of those points. Then using information from those two points, you can calculate point C. </p>
<p>This is what I used:
Point A = (1, 2.5)
Point B = (3, 7.5)
Point C = (3, 2.5)</p>
<p>Then, find the distances between lines AB, AC, and BC. You should get the answer to be 2, 5, and the square root of 29. The answer choice is A.</p>
<p>how'd u get these values: Point A = (1, 2.5)
Point B = (3, 7.5)
Point C = (3, 2.5)</p>
<p>do i just randomly choose a number between 4 and 1? since the slope is 5/2 for that line, if i go down 5, left 2, that would give me (5, 2)..so can that point be used on the triangle...but then, whats the purpose of finding that point. I dont get how u got those points.</p>
<p>Yeah, the problem is pretty much by trial and error for me and working with the answer choices. </p>
<p>The two points on the line have to have an x value of either 1, 2, 3. So, you would plug those x values into the equation y=5/2x to get the points. You would just use the points produced by plugging in 1 and 2, 1 and 3, or 2 and 3...to see which ones would work. Remember that by using those points you can find the points of C too.</p>
<p>Maybe this explanation is clearer.</p>
<p>How can we determine a slope of the line AB?
We can use any pair of points to calculate rise over run.
Let's take points A and B. The slope is BC/AC.
Now let's check out another pair of points: (4, 10) and (0,0).
The slope is (4-0) / (10-0) = 4/10 = 2/5.
That means that BC/AC = 2/5.
Only two pairs satisfy this condition: answers (A) and (B).</p>
<p>In triangle ACB <ACB=90 deg, so AC^2 + BC^2 should be equal AB^2.
Which triplet works?
For (A):
2^2 + 5^2 ?? (root 29)^2
4 + 25 = 29. These number do work!<br>
There is no need to test (B) - only one answer can be correct.
(A) is the answer.</p>
<p>Ubiquitous "hope this helps".</p>
<p>^
I am pretty beat and not very coherent: a tough final stretch before May 5.
I meant the slope is 5/2. :o</p>
<p>yeah i just solve it first by eliminating all the ones that dont fit a^2 + b^2 = C^2. </p>
<p>hen looking at the slope and seeing that the ratio of the vertical side to the horizontal side has to be 5:2. by process of elimination A is right.</p>
<p>Right, that works too, but it's twice the labor, because A, C, D and E answers all fit Pythagorean.
By the way, a part of this question is similar to 745/8 - in 860/18 we are looking for the slope in B, and in 745/8 - in (h,k).</p>