Ou are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is y=-8/3+8 . There is a tree in your yard at the point (3,16) . Each unit in the coordinate plane represents 1 foot. Approximately how far away is the tree from the zip line? Round your answer to the nearest tenth.

9514 1404 393

  5.6 feet

Step-by-step explanation:

Assuming your zip line equation is supposed to be ...

  y = -8/3x +8

we can rewrite it to general form:

  8/3x +y -8 = 0

  8x +3y -24 = 0 . . . . multiply by 3

Now, we can use the formula for the distance from a point to a line:

  d = |ax +by +c|/√(a²+b²) . . . . . distance from (x, y) to ax+by+c=0

Filling in the values we know, we have ...

  d = |8(3) +3(16) -24|/√(8² +3²) = 48/√73 ≈ 5.6

The distance from the tree to the zip line is about 5.6 feet.

if x = 1, then the answer is 3.5

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: