Transformation Rules
Identify the algebraic rule that would translate a
figure 3 units left and 2 units up.
R(x,y) --> (x+3, y+2)
H(x,y) --> (x-3, y+2)
N(x,y) --> (x+3, y-2)
M(x,y) --> (x-3, y-2)
H(x,y) --> (x-3, y+2)
Find the midpoint of the segment with endpoints
(-5, -3) and (-3, -1).
Midpoint:
(-4,-2)
What is your scale factor if your ratio is 2:5?
2/7
What are the three types of triangle classifications by side and angle? Define each.
Sides: Scalene, Isosceles, Equilateral
Angle: Acute, Obtuse, Right
Write the equation of a circle with center (-2,1) and has a radius of 8.
(x+2)2 + (y-1)2 = 64
Identify the algebraic rule that would dilate a
figure by a scale factor of 3 about the orgin.
R(x,y) --> (3x, y)
H(x,y) --> (x, 3y)
N(x,y) --> (3x, 3y)
P(x,y) --> (x/3, y/3)
N(x,y) --> (3x, 3y)
Find the distance between (-3, 6) and (9, -5).
d = 16.28 units
What is your scale factor if your ratio is 1:1?
1/2
What do you need to prove in order to prove a quadrilateral is a square?
Must prove:
2 sets of opposite parallel sides
4 congruent sides
4 right angles
or
Diagonals Bisect, Perpendicular and Congruent
Graph the following circle.
(x+1)2 + (y-4)2 = 4
Check graph
How would the following rule transform a figure?
H(x,y) ---> (-x, y)
a. Translation one unit left.
b. Reflection across the x-axis.
c. Reflection across the y-axis.
d. Reflection across y=x.
The midpoint of 𝑋𝑌 is point 𝑀(−4, 5). If the coordinates of X are (4, −3), what are the coordinates of Y?
Y(-12, 13)
Given the points A (-1, 8) and B (7, 10), find the coordinates of the point P on the directed line segment 𝐴𝐵̅ that partitions 𝐴𝐵 in half.
(3, 9)
Triangle ABC has the following vertices. A(-2, -1) B(-5,4) C(1,4). Classify the triangle by its side lengths, then tell me if its a right triangle.
Triangle ABC is Isosceles and does not have opposite reciprocal slopes. Therefore, it is not a right triangle.
Write the equation of a circle with center (0,3) and has a point on the edge of the circle at (3,7)
Using point A(-3,7) as your preimage. What is the image of point A after it is rotated 90 degrees CCW about the origin?
a. A'(3,7)
b. A'(-7,-3)
c. A'(-3,-7)
d. A'(7,3)
b. A'(-7,-3)
On a map, Julie’s house is located at (−2, 1) and Jimmy’s house is at (4, −2). How long is the direct path from Julie’s house to Jimmy’s house?
d = 6.71 units
Given A (6, -10) and B (9, -1), find the coordinates of point P on 𝐴𝐵 so that P partitions 𝐴𝐵 in the ratio 1:2.
(7,-7)
Prove that quadrilateral A(-4, 3), B(2, 7), C(5, 1), and D(-1, -3) is a parallelogram.
Slopes: AB//CD and BC//AD
AB= 6/4 =2/3
CD= -4/-6 =2/3
BC= -6/3 =-2
AD= -6/3 =-2
Find the center and radius of the following circle equation:
x2+6x+9+y2-4y+4=169
Center: (-3,2)
Radius: 13
Using point A(-3,7) as your preimage. What is the image of point A after it is translated 4 units to the left and 5 units up then reflected across the x axis?
a. A'(1,12)
c. A'(-7,-12)
b. A'(-7,12)
d. A'(-7,2)
c. A'(-7,-12)
The Riley and Brown families decided to go to a concert together. The Riley’s live 6 miles west and 3 miles north of the concert. The Browns live 2 miles east and 4 miles south. How far apart do they live?
d = 10.63 miles
Given A (-10, -3.5) and B (2, 5.5), find the coordinates of point P on 𝐴𝐵 so that P partitions 𝐴𝐵 in the ratio 5:1
Prove that ABCD is a square. A(2,4) B(5,3) C(4,0) D(1,1)
ABCD is a square. Evidence must be shown!
Here is an equation of a circle: x2+y2-16x+4y+43=0
Find the center and radius by completing the square.
Center: (8,-2)
Radius: 5