Grayson is designing a rectangular athletic field. On his scale drawing, the vertices of the rectangle are (4,5), (9,10), and (9,5). What are the coordinates of the fourth vertex?
We can start by drawing a sketch of the rectangle using the given vertices:
```
(4,5) (9,5)
.-----------.
| |
| |
| |
.-----------.
(9,10)
```
To determine the coordinates of the fourth vertex, we can observe that each side of the rectangle is parallel to either the x-axis or the y-axis. Therefore, we can use the coordinates of the two vertices on each side to determine the length and direction of the side, and then extend that side to find the missing vertex.
For example, the left side of the rectangle is parallel to the y-axis and runs from (4,5) to (9,5), so we know that the missing vertex must also have a y-coordinate of 5. To determine its x-coordinate, we can calculate the length of the side as:
9 - 4 = 5
Therefore, the missing vertex must be 5 units to the right of (9,5), which gives us:
(9+5, 5) = (14, 5)
Similarly, we can apply this process to the other two sides of the rectangle to find the coordinates of the missing vertex:
- The top side runs from (9,5) to (9,10), so the missing vertex must have an x-coordinate of 9 and a y-coordinate that is 5 units above 10:
(9, 10+5) = (9, 15)
- The right side runs from (9,10) to (4,5), so the missing vertex must have a y-coordinate of 10 and an x-coordinate that is 5 units to the left of 4:
(4-5, 10) = (-1, 10)
Therefore, the coordinates of the fourth vertex are:
(14, 5), (9, 15), (-1, 10)
Grayson is designing a rectangular athletic field. On his scale drawing, the vertices of the rectangle are (4,5), (9,10), and (9,5). What are the coordinates of the fourth vertex?
A. (4,9)
B. (4,10)
C. (5,10)
D. (5,9)
None of the answer choices match the coordinates of the fourth vertex. The correct answer is (14, 10).
Which ordered pair is not a solution of y=-12x-3?
A. (-3,33)
B. (8,-98)
C. (-9,105)
D. (3,-39)
We can check each ordered pair by substituting the x and y values into the equation y = -12x - 3 and seeing if the equation is true.
A) (-3, 33):
y = -12x - 3
33 = -12(-3) - 3
33 = 36 - 3
33 = 33
This equation is true, so (-3, 33) is a solution.
B) (8, -98):
y = -12x - 3
-98 = -12(8) - 3
-98 = -96 - 3
-98 = -99
This equation is not true, so (8, -98) is not a solution.
C) (-9, 105):
y = -12x - 3
105 = -12(-9) - 3
105 = 108 - 3
105 = 105
This equation is true, so (-9, 105) is a solution.
D) (3, -39):
y = -12x - 3
-39 = -12(3) - 3
-39 = -36 - 3
-39 = -39
This equation is true, so (3, -39) is a solution.
The only ordered pair that is not a solution of y = -12x - 3 is answer choice B, which is (8, -98). So the answer is B.
Which is the graph of the linear equation y=-1/4x+3?
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Comparing y = -1/4x + 3 to y = mx + b, we see that the slope is -1/4 and the y-intercept is 3.
Using this information, we can plot the y-intercept at (0, 3) and then use the slope to find additional points on the line.
To find another point on the line, we can move down 1 space (since the slope is negative and the denominator is 4) and right 4 spaces (since the numerator is 1), giving us the point (4, 2). We can continue this pattern to find more points on the line.
Here is a graph of y = -1/4x + 3:
```
|
4 + .
| .
| .
| .
2 +
|
|
+------------------
0 1 2 3 4
```
The answer is option A.
Find three solutions of the equation.
y=2x-6
A. (-2,-10),(1,-4),(2,-1)
B. (-2,-10),(1,-4),(0,-6)
C. (0,-6),(3,-2),(-2,-10)
D. (1,-4),(0,-6),(-1,-9)
We can find any number of solutions for an equation of the form y = 2x - 6 by choosing different values of x and computing the corresponding values of y using the equation.
For example, if we set x = -2, we get:
y = 2x - 6
y = 2(-2) - 6
y = -4 - 6
y = -10
So one solution is (-2, -10).
Similarly, if we set x = 1, we get:
y = 2x - 6
y = 2(1) - 6
y = 2 - 6
y = -4
So another solution is (1, -4).
Finally, if we set x = 2, we get:
y = 2x - 6
y = 2(2) - 6
y = 4 - 6
y = -2
So a third solution is (2, -2).
Therefore, the answer is not one of the given choices.
Determine which pair of points has a positive slope.
A. (5,-4),(-2,1)
B. (-10,-2),(6,6)
C. (6,-10),(2,10)
D. (5,-1),(-6,6)