XYZ vertices X(5,6),Y(9,12), and Z(12,8). It’s translated right 8 units and up 3 units. What are the coordinates of X’,Y’,Z’
The new coordinates of X' would be:
X'(5+8,6+3) = (13,9)
The new coordinates of Y' would be:
Y'(9+8,12+3) = (17,15)
The new coordinates of Z' would be:
Z'(12+8,8+3) = (20,11)
Therefore, the translated vertices are X'(13,9), Y'(17,15), and Z'(20,11).
The point is reflected across the y-axis. Use arrow notation to describe the original
point and its reflection.
Let's say the original point is P and its coordinates are (x,y). The arrow notation for the original point would be:
P(x,y) →
After reflecting the point across the y-axis, the new coordinates become (-x,y). Therefore, the arrow notation for the reflected point would be:
P'( - x, y) ←
The point Q(9,-1)is reflected across the y-axis. Use arrow notation to describe the original
point and its reflection.
The original point is Q(9,-1), and its arrow notation is:
Q(9,-1) →
When Q is reflected across the y-axis, the x-coordinate changes sign. Therefore, the coordinates of its reflection Q' are (-9,-1), and the arrow notation for the reflected point is:
Q'(-9,-1) ←
The table shows the amount of money Angelica earned based on the number of hours she
worked.
Angelica's Pay
Hours Worked (h) Amount Earned (A)
3 $22.50
8 $60.00
15 $112.50
Which equation best represents Angelica's pay?
(1 point)
A = 7.50h
A = 22.50h
A = h + 7.50
To determine the equation that represents Angelica's pay, we can observe that when the number of hours worked triples (from 3 to 9), the amount earned also triples (from $22.50 to $67.50). This tells us that the amount earned is directly proportional to the number of hours worked.
Using this information, we can write the equation:
A = kh
where k is the constant of proportionality. To find k, we can use any of the given data points. For example, using the first data point (h=3, A=$22.50):
22.50 = k(3)
k = 7.50
Therefore, the equation that best represents Angelica's pay is:
A = 7.50h
So, option A (A = 7.50h) is the correct answer.
Point A(4, 2) is translated according to the rule (x, y) (x + 1, y – 5) and then reflected across
the y-axis.
a) In which quadrant of the coordinate plane is point A located?
b) What are the coordinates of translated point A’? In which quadrant of the coordinate
plane is point A’ located?
c) What are the coordinates of reflected point A’’? In which quadrant of the coordinate
plane is point A’’ located?
To translate a point in the coordinate plane, you need to add or subtract the same value to both the x-coordinate and the y-coordinate of the point.
In this case, the given translation is right 8 units and up 3 units.
To find the new coordinates of each point:
For point X(5,6), add 8 to the x-coordinate and add 3 to the y-coordinate.
New coordinates of X' = (5 + 8, 6 + 3) = (13, 9)
For point Y(9,12), add 8 to the x-coordinate and add 3 to the y-coordinate.
New coordinates of Y' = (9 + 8, 12 + 3) = (17, 15)
For point Z(12,8), add 8 to the x-coordinate and add 3 to the y-coordinate.
New coordinates of Z' = (12 + 8, 8 + 3) = (20, 11)
Therefore, the coordinates of X’, Y’, and Z’ are (13, 9), (17, 15), and (20, 11) respectively.