As you leave clark, the sign says lutherville 145 miles, otisburg 195 miles. if the planet diner is halfway between lutherville and otisburg, how far is it from clark?

Therefore Planet Diner is located 170 miles from Clark.

Step-by-step explanation:

We are given our origin, which is Clark (C) and three Locations as Lutherville (L), Otisburg (O) and Planet Diner (PD).

We know that the distance between Clark and Lutherville is 145 miles.

We know that the distance between Clark and Otisburg is 195 miles.

We also know that Planet Diner is halfway between Lutherville and Otisburg, thus exactly in between them.

So if we can find the position of Planet Diner between Lutherville and Otisburg,  we will automatically know its distance from Clark, since Clark is the reference origin for ALL locations.

Thus we have

Therefore Planet Diner is located 170 miles from Clark.

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: