Foundations of Geo
What is the midpoint of the segment joining (2, 3) and (6, 7).
(4, 5)
what is the slope of the line that is perpendicular to the line formed by (1,5) and (-2,-4)?
-1/3
Select all the transformations that preserve distance.
A. (x, y)→(x, -y)
B. (x, y)→(10x, 10y)
C. (x, y)→(x+5, y-8)
D. (x, y)→(-y, x)
E. (x, y)→(0.2x, 0.2y)
A,C,E
In a right triangle, the length of the shortest side is 9 units, the length of the long side is 12 units, how long is the hypotenuse?
15 units
Name a quadrilateral with exactly one pair of parallel sides.
Trapezoid
Write the converse of the statement: "If it is raining, then the ground is wet."
If the ground is wet, than it is raining.
Function f has the following coordinates: (0,5), (1,7), (2,9), and (3,11).
Function g has the following coordinates: (0,10),(1,15), (2,10), and (3,25)
Are the lines parallel, perpendicular, or neither? why?
Neither. f(x) has a slope of 2 and g(x) has a slope of 5
Given the points Q(1,4), R(3,-2), S(0,-1) and T (-2,2). Find the coordinates of S after a reflection across y=0, then a translation 1 unit left and 2 units up
What type of triangle is formed by the following side lengths:7cm, 10cm, 12cm
Acute
KRMW has vertices at K(-3, 4), R(-5, 2), M(-3, 2), and W(-1, 4). What quadrilateral classification does KRMW have
parallelogram
What are the coordinates of the point 3/4 of the way from A(-6,-3) to B (10,9)?
( 6,6)
<1 and <2 are alternate exterior angles, if m<1=(3x+8) degrees and m<2=(5x-4) degrees. What is the value of x? and how many degrees is each angle?
x=6, each angle measures 24 degrees
Which transformation or sequence of transformations maps triangle ABC to triangle A'B'C'?
A ( 5,5), B(1,3), C (2,1)
A' (0,-5) B(-4,-3) C'(-3,-1)
A Translation 5 units left, then a reflection across y=0
A graphic designer is making a triangular logo, ∆XYZ, with vertices X(4, -1), Y(5, 6), and Z(1, 3).What Triangle describes the logo ( classify by side and angle)
Right Isosceles
Consider: Trapezoid RCZM with midsegment LF
Given RC=3x, LF=5x-2, and MZ=4x+2, find the value of x.
2
Ray JK bisects ∠RJT, such that the measure of ∠RJK = (25x-6)° and the measure of ∠KJT = (15x+8)°.
29 degrees
Write the equation of a line perpendicular to
y = -2x + 5 that passes through (4, -3).
y= (1/2)x-5
∆NPK has an area of 32 square centimeters . ∆NPK is dilated using a scale factor of k=1/2 to form ∆WXY. What is the area of ∆WXY?
8 square centimeters
Given a triangle with sides x, 14, and 2x+1. What is the minimum value of x?
5
KLMN is a rectangle with diagonals that intersect at point E. (KE) ̅=3x-7 and (LN) ̅=2x+2. Determine the length of (LE) ̅.
5
Given: ∠1 and ∠2 are complementary and ∠3 and ∠2 are complementary. Prove: ∠1 ≅ ∠3
1. m<1 +m<2 =90 ------ given
2. m<3+m<2= 90--------- given
3. m<1 +m<2 = m<3 + m<2 ---- substitution
4. m<1 = m<3 ----- subtraction property of equality
5. <1 is congruent to <3---- definition of congruence
For the points A (-3,2), B(-3,6), and C (-1,6), find the slope of the line through B perpendicular to line AC.
-1/2
Given triangle ABC: A (2,4), B(1,1), (4,3). What are the coordinates of A'B'C' after a rotation of 180 degrees clockwise and a translation of 1 unit to the left and 2 units down?
A'( -3,-6) B'(-2,-3), C'(-5,-5)
Madisyn is planting crops in a triangular garden. She is trying to find the amount of fencing she needs to block off the crops from animals. The triangular garden, ABC, is formed by the following points A(0,6), B(6,5), and C(5,-1). To the nearest tenth, what is the amount of fencing that Madisyn needs?
20.8 units
Kite NBAF has vertices at N(6, 4), B(2, 7), A(-5, 4), and F(2, 1). What is the area of kite NBAF, is square units?
33 units