Ambiguous official ACT practice question?

Test Preparation
1

<p>So I was doing the math section on the official ACT free practice test (<a href="http://www.act.org/aap/pdf/preparing.pdf%5B/url%5D"&gt;http://www.act.org/aap/pdf/preparing.pdf&lt;/a> btw the question I'm talking about is on like page 30 of that PDF).</p>

<p>It's #59 on the test.</p>

<p>What I did was the distance formula between the three lines of the triangle, sgrt((X2-X1)^2-(Y2-Y1)^2) for each of the lengths of the triangle. After the calculating, I got 4 for the base, 4 for the hypotenuse-thing, and sqrt5 for what I think is the height. It's asking for the area, so I did .5 (4 times sqrt5) and got 4.47.</p>

<p>This didn't really match up with the choices, which were 4,5,4sqrt2, 4sqrt3, 8, and 8sqrt2.
The answer is 4.</p>

<p>Did I assign the height wrong? Was I supposed to multiply 4 by the hypotenuse-looking thing, which is also 4? That would give me 4 on the dot. Or did I do it right originally, and I was simply supposed to round down?</p>

2

<p>This problem is really a lot easier than you are making it. The area of a triangle is base x height / 2. The base is clearly (5 - 1) = 4. The height is clearly (5 - 3) = 2. Thus A = 4 x 2 / 2 = 4. Height refers to the length of the shortest line segment between the vertex opposite the base and the line on which the base lies.</p>

<p>Don’t round.</p>

3

<p>Not sure if this was a typo, but distance = sqrt[((x2-x1)^2)+((y2-y1)^2)] You had a minus sign in between the two terms.</p>

<p>Another way you could do it (I didn’t try it so the numbers could be rough) is finding the distance of AB and AC then use Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2 and a, b, and c are the lengths of the sides of the triangle.</p>

4

<p>Oh shoot… I didn’t see aegrisomnia’s post before I posted my response. Now I look silly because I didn’t even realize you could do the problem his/her way. Def follow that advice and not mine.</p>

5

<p>aegr- :expressionless: Oh. Lol. I guess I can just attribute this to trying to be too clever.</p>