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# CAHSEE practice: Problems 38-42

Video transcript

Problem 38. In the drawing below, the figure
formed by the squares with sides that are labeled x,
y, and z is a right triangle. So the figure, so it's
a right triangle. And then they ask us, which
equation is true for all values of x, y, and z? So really, they're just trying
to see if you remember the Pythagorean Theorem. And that just tells us that if
we have a right triangle, that the sum of the squares of the
two smaller sides, so x squared plus y squared, is
going to be equal to the square of the longest side, or
the side that's opposite the right angle. Or we also call that
the hypotenuse. So that's equal to z squared. That's what the Pythagorean
Theorem tells us. And so if we look down here,
only one of those match what I just wrote down, are kind
of my restatement of the Pythagorean Theorem. x squared plus y squared
is equal to z squared. And that's this one right
there, choice B. Next problem. Problem 39. A clothing company created the
following diagram for a vest. So I guess this is somehow a
vest. Maybe it's half of the vest, because I don't see how
I could put that on me. To show the other side of the
vest-- OK, right, so this was half of the vest-- the company
will reflect the drawing across the y-axis. What will be the coordinates
of C after the reflection? So when they say reflection,
they mean, literally, just take the image of this and
you flip it over onto the right-hand side. So I could draw it out,
and draw it in blue. So if I take the reflection,
this line right here is at negative 1. It's 1 to the left
of the y-axis. So when I take its reflection,
I would draw it right here, 1 to the right of the y-axis. This line down here, it goes
from 1 to the left all the way to 4 to the left. On this side, it's going to go
from 1 to the right all the way to 4 to the right. I could keep doing it. This segment right here, FE,
when I flip it, will become this segment right here. This segment, DE, right here,
will become this segment. It'll just look something like
this when I go onto that side. And then C, right here, is 2
to the left of the y-axis. So C over here will be 2 to
the right of the y-axis. So it's going to look
something like this. So the vest is going to look
something like this. And then of course, it just
dips down like that. So that's the right-hand
side of the vest. But they want to know what
are the coordinates of C? So this is C, and this is the
C after the reflection. Maybe I could call it C prime. And so its coordinates are--
its x-coordinate is 2. And we're 2 to the right;
before, we were 2 to the left, at minus 2. And its y-coordinate is
going to be the same, it's going to be 7. 2, 7. So that is choice A. I'll do it in the next video. Well, there's only two problems
in this video. So let me go to the next page. Number 40. What is the area, in
square units, of trapezoid QRST shown below? So we need to figure out
the area of this. And they actually even
give us a formula. They gave us the formula
for this trapezoid. So they're calling it 1/2 times
the height, times base 1 plus base 2. So essentially, just to give you
an intuition of where this comes from, you're essentially
saying, what's the average width of this trapezoid? So you take 1/2 times the sum of
this guy and that guy, and that gives you the
average width. And then you multiply that
times the height. So just applying this formula,
it is 1/2 times my height-- my height is 8-- times base 1,
let's call this base 1, 20. Plus base 2. Base 2 is this 6 right there. So I have 1/2 times 8,
which is 4, times 26. And 4 times 26 is equal
to 104 square units. So that's that right there. So they're really just
testing whether you can apply this formula. Whether you can recognize what's
the height and what are the two bases. Problem 41. One millimeter is. Well, here they're just seeing
if you remember your units. Let me write it this way. Deci is equal to 1/10. Centi is equal to 1/100. And then milli is
equal to 1/1000. So one millimeter is
1/1000 of a meter. They're just making sure you
remember your metric prefixes. Problem 42. In the diagram below,
hexagon LMNPQR is congruent to hexagon STUVWX. Congruent just means all the
sides are equal and all the measures of their angles
are also equal. So they say, which side is
the same length as MN? So this is MN right there, and
we want to know what side is the same length as that. So let me make sure
that they're not trying to confuse us. So they start here, they
say LMNPQR, and then they say STUVWX. So they're not confusing us. These points do correspond. S corresponds to L, M
corresponds to T, and so forth and so on. So this segment is going to be
congruent to that segment right there. Segment TU. So MN is the same
length as TU. That is choice B.