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Coordinate plane word problem examples

Video transcript

Melina's town is built on a grid similar to the coordinate plane she is riding her bicycle from her home at point negative three comma four to the mall at point negative three comma negative seven each unit on the graph denotes one city block plot the two points and find the distance between Molina's home and the mall so let's see they tell her she's riding her bicycle from her home at the point negative three comma four so let's plot negative three comma four so now I'll use this point right over here so negative three is our x-coordinate so we're going to go three to the left of the origin one two three that gets us to negative three and positive four is our y-coordinates we're going to go four above the origin or ICC we're going to go four up so we're going to go four up so we went negative three over three to the left that's negative 3 positive 4 or you could say we went positive 4 negative 3 this tells us what we do in the horizontal direction this tells us what we do in the vertical direction now let's figure out that's where her home is now let's figure out where the mall is it's at the point negative 3 comma negative 7 so negative 3 we went 3 negative 3 along the horizontal direction and then negative 7 along the vertical direction so we get 2 negative 3 negative 7 right over there now we need to figure out the distance between her home in the mall now we could actually count it out or we could just compute if we wanted to count it out it's 1 2 3 4 5 6 7 8 9 10 11 blocks so we could type that in and another way to think about it is they have the exact same x axis the exact same x-coordinate they're both at the x coordinate negative 3 the only difference between these two is what is happening in the y coordinate this is at a positive 4 this is at a negative 7 positive 4 and negative 7 so we're really trying to find the distance between 4 and negative 7 so if I were to say 4 minus negative 7 we would get this distance right over here so we have 4 minus negative 7 which is the same thing as 4 plus 7 which is 11 let's do a couple more Carlos is hanging a poster in the area shown by the red rectangle he is placing a nail in the center of the blue line in the second graph in the second graph plot the point where he places the nail so he wants to place a nail on the center of the blue line so the center of the blue line the blue line is six units long the centers right over here that's three to the right three to the left so he wants to plot he wants to put the nail at the point x equals zero Y is equal to four so he wants to put it at X is equal to zero Y is equal to four that's this point right over here so let's check our answer let's do one more a town town a and town B are connected by a train that has a station at the point negative one comma three I see that the train tracks are in blue fair enough which town is closer to the station along the train route town a or town B so they're not just asking us what's the kind of crows flight the distance the distance that if you were to fly they're saying the distance which town is closer to the station along the train route so if you were to follow the train route just like that so the a right over here a has you have to go if you were going along the train route you would have to go one two three four five six in the X direction and then one two three four five along the y direction so you'd have to go a total of eleven if you're going from B you're going one two three four five six seven eight nine ten eleven along the x direction and then one two three four five six so six along the vertical direction so you going to go total 17 so it's pretty close it's pretty obvious that a is closer along the tracks now you could also think about it in terms of coordinates because the a is at the coordinate negative 7 comma 8 and if you were to think about negative seven comma 8 to get from negative seven to negative one along the x coordinates you're going to go six and then to go from eight to three you're going to go five more so you could also not necessarily count it out you can actually just think about the coordinates but either way you see that town a is closer