Geometry questions will cover: midpoints, x and y intercepts, slope, arcs, chords, cones, and triangles.
Example 1:
Find the coordinates (x, y) of the midpoint of the line segment on a graph that connects the points (5, 2) and (1, -10).
Solution 1:
In order to find midpoints on a line, you need to use the following formula:
For two points on a graph (x1, y1) and (x2, y2), the midpoint is:
(x1 + x2) ÷ 2 , (y1 + y2) ÷ 2
Now calculate for x and y:
(5 + 1) ÷ 2 = midpoint x, (2 + -10) ÷ 2 = midpoint y
(6) ÷ 2 = midpoint x, (-8) ÷ 2 = midpoint y
- 3 = midpoint x, - 4 = midpoint y
(3,-4)
Example 2:
Consider the vertex of an angle at the center of a circle. The diameter of the circle is 4. If the angle measures 90 degrees, what is the arc length relating to the angle?
Solution 2:
To solve this problem, you need these three principles:
(1) Arc length is the distance on the outside (or circumference) of a circle.
(2) The circumference of a circle is always p times the diameter.
(3) There are 360 degrees in a circle.
The angle in this problem is 90 degrees.
360 ÷ 90 = 4
In other words, we are dealing with the circumference of 1/4 of the circle.
Given that the circumference the circle is 4p, and we are dealing only with 1/4 of the circle, then the arc length for this angle is:
4p ÷ 4 =
p
Example 3:
You will have at least one question on combinations or permutations.
How many 2 letter combinations can be made from the letter set: H A N D Y?
Solution 3:
To determine the number of combinations of S at a time that can be made from a set containing N items, you need this formula:
(N ! ) ÷ (N - S) ! ´
S !
In the example above, S = 2 and N = 5 (because there are five letters in the set).
Now substitute the values for S and N:
(5 ´ 4 ´ 3 ´
2 ´
1) ÷ ((5 - 2) ! ´ (2 !) =
(5 ´ 4 ´ 3 ´
2) ÷ ((3´
2 ´
1) ´ (2 ´
1) =
120 ÷ 12 = 10
So 10 two-letter combinations can be made from a five letter set.
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