Hey guys could you help me with these ACT maths practice questions? These questions are from the 2015/2016 free practice test made by the ACT.org.
I trapezoid with coordinates A(2,1) B(3,4) C(9,4) and D(12,1) is given:
41.Which of the following vertical lines cuts ABCD into 2 trapezoids with equal areas?
A. X= 2.5
B. X= 3.5
C. X= 4.5
D. X= 5.5
E. X= 6.5
The points E(6,4) and F(14,12) lie in the standard (x,y) coordinate plane. Point D lies on EF between E and F such that the length of EF is 4 times the length of DE. What are the coordinates of D?
F. (7,5)
G. (8,6)
H. (8,8)
J. (10,8)
K. (12,10)
45. I couldn't right the question properly cause it's a matrix questions. If you guys have the test with you.. My be u can help?
A. 4/3
B. 27/2
C. 26
D. 27
E. 28
46.A container is 1/8 full of water. after 10 cups of water are added, the container is 3/4 full. What is the volume of the container, in cups?
F. 13 1/3
G. 13 1/2
H. 15
J.16
K.40.
The area of a trapezoid is 1/2 times the sum of its bases times its height. We don't actually care about the height here because the height is constant if we cut into two trapezoids). So we are looking for the value k such that x = k cuts trapezoid ABCD into two trapezoids such that the sum of the bases of either trapezoid is the same.
The sum of the bases of trapezoid ABCD is 10+6 = 16, so we want the sum of the bases of either trapezoid to be 8. Choice E does this since the left trapezoid would have sum of bases = (6.5 - 3) + (6.5 - 2) = 8.
Informally, D is 1/4 of the way from E to F. Because EF is a line, one way to find the coordinates is note that the x-coordinate must be 1/4 of the way from 6 to 14, and the y-coordinate must be 1/4 of the way from 4 to 12. Then D is at (8,6), G.
a = 27/6 = 9/2 since a6 = 27 (look at the 1st row, 2nd column). Then x+z = (27/6)(2+4) = 27, D.
10 cups of water occupy 5/8 of the container. So 16 cups of water occupy the whole container, J.
