Distance Formula
What is the distance between points M( - 3, - 1) and N(2, 3)?
√41
If point M is the midpoint of the line segment PQ, and the line segment PM is 6 centimeters, what is the length of PQ?
12 centimeters
What is the contrapositive of the following statement?
If a triangle is isosceles, then it has two congruent sides.
If a triangle does not have two congruent sides, then it is not isosceles.
d = Kane wins the scientific decathlon
n = Kane scores > 90% in biology class
What does n ∧ d represent?
Kane scores >90% in biology class and wins the scientific decathlon.
Parallelograms have two pairs of parallel sides. Some trapezoids are parallelograms. Therefore...
Some trapezoids have two pairs of parallel sides.
What is the approximate distance between the points ( - 13, 8) and (206, 196) in the xy-plane?
289 units
Find the coordinates of the midpoint of the line segment whose endpoints are (2, - 6) and (10, 4).
( 6, - 1)
- N < O
- L is not the smallest
- L is between M and N
Find the order from left to right.
M L N O
Let p represent "x is prime," and let q represent "x is even." Which statement is true if x = 2?
a) ~p ∧ q
b) ~q ∧ p
c) p ∧ q
d) ~(p ∧ q)
c) p ∧ q
**Special, Slide #3***
p ∧ ~q
Points A(0,4), B(0,0), and C(3,0) form a right triangle. What is the length of the hypotenuse?
5
The coordinates on a grid of the location of 2 trees in a park are (3,9) and (5, 3) . What are the coordinates of the midpoint of the line segment joining the 2 trees?
Consider this statement:
If you did not have a ticket, you could not win the Lotto.
Which of the following has the same meaning as the statement above?
I. If you won the Lotto, then you must have a ticket.
II. If you have a ticket, you will win the Lotto.
III. Lotto winners come from ticket holders.
I and III
**Special, Slide #2**
1) D
2) A
3) B
4) C
A teacher makes the statement, "If all students pass this test, then there will be no homework on Friday." What statement would indicate the teacher did not follow through with this statement?
All of the students passed the test and they had homework on Friday.
Scott's house is located 7 miles east and 5 miles north of Origin High School, O.
Jill's house is located 5 miles west and 9 miles north of Origin High School.
To the nearest tenth of a mile, what is the shortest distance between Scott's house and Jill's house?
12.6 miles
An archaeologist used string to make a grid over an area where she was digging. She discovered a bowl buried at (1, 4) and a tool at (3, 10)on her grid. She suspected that an item was buried at the midpoint of the segment connecting the bowl and the tool. At which position on her grid should the archaeologist dig to look for the buried item?
( 2, 7)
"If pi is an integer, then the square root of 9 is not a whole number."
Which of the following statements is neither converse, inverse, nor contrapositive of the statement given above.
a) If pi is not a whole number, then the square root of 9 is not an integer.
b) If the square root of 9 is a whole number, then pi is not an integer.
c) If the square root of 9 is not a whole number, then pi is an integer.
d) If pi is not an integer, then the square root of 9 is a whole number.
(a) If pi is not a whole number, then the square root of 9 is not an integer.
The following is an example of which law?
x → t
t → z
∴ x → z
Law of Syllogism
Which statement is always true?
a) p ∧ ~p
b) ~(~p) ↔ p
c) p → ~p
d) p ∧ q
b) ~(~p) ↔ p
**Special, Show Slide #1**
85 yards
In a circle, the coordinates of the endpoints of a diameter are (4,5) and (10, 1). What are the coordinates of the center of the circle?
( 7, 3)
Match each statement in section 1 with a statement in section 2 which has the same meaning.
Section 1a) 19-year-olds can vote.
b)If you can vote, then you are 19.
c) If you are not 19, then you can vote.
Section 2
1) If you cannot vote, then you are 19.
2) If you are not 19, then you cannot vote.
3) If you cannot vote then you are not 19.
A and 3
B and 2
C and 1
**Special, Slide #4***
a)
1) x is not divisible by 3 or x is a prime number.
2) If x is an even integer, then x is divisible by 3.
b)
1) p ↔ r
2) (q ∧ r) → p
c) If x is not a prime number, then x is an even number.
**Special, Slide #5**
1) F
2) T
3) T
4) F
5) T