Help with these EASY Math problems!!

Test Preparation SAT Preparation
1

<p>The centroid of a triangle is the point which is found 2/3 of the distance from a vertest to the midpoint of the opposite side. In the standard (x,y) coordinate plane below, TRIANGLEABC is shown with centroid G. What are the coordinates of G?</p>

<p>a (3,8) (b) (0,3) (c)6,1</p>

<p>answers</p>

<p>F (3,2)
G(3,4)
H(2,6)
J(4, 20/3)
K(6,6)</p>

<p>What is the area of the largest circle that can be isncribed in a semicircular region of radius R?</p>

<p>A pi-r squared /4
B pi r squared/ 3
C pi r squared/ 2
D 2/3 pi r squared
E 3/4 pi r squared</p>

<p>If a circle with center at the origin passes through (0,5) through which of the following dose it also pass</p>

<p>A 2,square root of 21
B 4 ,5
C 5, square root of 21
D 5 5
E 5 12</p>

2

<ol>
<li>The centroid is also at the intersection of any two of the medians. The midpoint of AC is (4.5, 4.5), and using the slope-intercept method the equation of the median that goes through that point and B(0,3) is y = (1/3) x + 3. The midpoint of BC is (3,2) and the equation of the median that goes through it is x = 3. The intersection point of these two lines is (3,4). That’s the centroid; answer G.</li>
</ol>

3

<ol>
<li>Pretty clearly the largest circle you can inscribe in a semicircle is the one that goes all the way to the top of it. That circle has radius R/2, and area pi* (R/2)^2. Answer A.</li>
</ol>

4

<ol>
<li> A circle centered at the origin has equation x^2 + y^2 = R^2. Clearly R=5 in order for (0,5) to lie on the circle. So (x,y) has to satisfy x^2 + y^2 = 25, and only choice A does that.</li>
</ol>

5

<p>These questions probably belong to the SAT II Math 2.</p>

<p>Question 1.
Centroid G of a triangle is also its center of gravity (center of mass).</p>

<p>Cool facts to know.
In 1, 2, and 3 dimensions the coordinates of G of respectively
segment AB,
triangle ABC,
and tetrahedron ABCD
are the averages of the corresponding coordinates of points
A and B,
A, B, and C,
A, B, C, and D.</p>

<p>Examples.
[1] For A(3) and B(-5) (3+(-5))/2=-1, so G(-1) (duh).</p>

<p>[2] For A(3,8), B(0,3), and C(6,1)
(3+0+6)/3=3, (8+3+1)/3=4, thus G(3,4) - answer G in question 1.</p>

<h1>[3] Who cares :)</h1>

<p>Question 3.
Since the radius of the circle, as greennblue rightfully noted, is 5, if one of the coordinates of a point on this circle is 5, the other one should be 0.
That rules out choices B, C, D, and E.</p>