A ball game between Dylan and Mya is about to begin. Using sidewalk chalk, they draw their “arena” on the ground. The arena can be modeled by the equation x/2 + y/2 = 81 . Dylan has taken his position at (-5, -2) and Mya has taken her position at (6, 4). Each graph unit represents 1 meter.
what are the points
To find the points on the graph that represent the arena, we need to solve the equation x/2 + y/2 = 81 for different values of x and y.
First, let's solve for x when y = 0:
x/2 + 0/2 = 81
x/2 = 81
x = 81 * 2
x = 162
So, one point on the graph is (162, 0).
Next, let's solve for y when x = 0:
0/2 + y/2 = 81
y/2 = 81
y = 81 * 2
y = 162
Another point on the graph is (0, 162).
Finally, let's find the y-intercept:
0/2 + y/2 = 81
y/2 = 81
y = 81 * 2
y = 162
So the y-intercept is (0, 162).
Putting it all together, the three points on the graph that represent the arena are:
- (162, 0)
- (0, 162)
- (0, 162)
How far apart are Dylan and Mya (to two decimal places)?
To find the distance between two points, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between Dylan's position (-5, -2) and Mya's position (6, 4):
d = √((6 - (-5))^2 + (4 - (-2))^2)
= √((6 + 5)^2 + (4 + 2)^2)
= √(11^2 + 6^2)
= √(121 + 36)
= √157
≈ 12.53
So, Dylan and Mya are approximately 12.53 meters apart.