Finding the Coordinates of a Point In Exercises 8, find the coordinates of the point. The point

Finding the Coordinates of a Point In Exercises 8, find the...

Key Concepts

Cartesian Coordinate System

The Cartesian coordinate system is a framework for representing points in a plane using two perpendicular axes, typically labeled as the x-axis (horizontal) and the y-axis (vertical). Each point is identified by an ordered pair (x, y) that represents its horizontal and vertical positions in relation to the origin.

Axes and Their Roles

The x-axis and the y-axis serve as the fundamental reference lines in the plane. The x-axis represents horizontal movement, while the y-axis represents vertical movement. Understanding that points on the x-axis have a y-coordinate of zero and points on the y-axis have an x-coordinate of zero is key to determining positions accurately.

Negative Numbers in Coordinate Geometry

Negative numbers in coordinate geometry indicate direction relative to the origin. A negative value on the x-axis signifies a position to the left of the origin, which is a critical concept for determining a point's exact location when given a distance or direction in a particular orientation on the plane.

Transcript

00:01 Okay, so our question is asking for us to find the coordinates of the point that is on the x -axis and is 12 units to the left of the y -axis so for a problem like this, the first thing i would do is i would draw it out draw a picture so that i can see what i'm working with so and before we even look at this problem in particular, let's make sure we understand what the x and y coordinates are and what they need i like to think about the x and coordinate, the x and y coordinates as starting at this little point in the center.

00:41 This is called the origin, and this is where both x and y are zero.

00:46 I like to think about starting here at my little zero, zero, and then to get to my point, i think how far to the right or left did i move for the x coordinate, and then how far up and down do i move for the y coordinate? so just as an example, if i were to put a point right here, then to find my x -cordinate, i would think how far did i move if i'm only allowed to go side to side.

01:20 So i'm going to start at this, at the origin, and then if i'm locked on the x -axis, i'm not allowed to move up and down.

01:28 I'm just going to see how far i moved to the side.

01:32 And clearly for this point, i move to the left.

01:35 So let's see how many spaces.

01:36 One, two, three, four, five spaces to the left.

01:41 So that tells me that my x -coordinate is going to be negative five.

01:50 To find the y -cordinate, i'm going to do that same thing, but this time i'm going to pretend that i'm locked on the y -axis, and i'm only allowed to go up and down.

02:00 So i'm going to start at the origin and i'm going to count one, two.

02:06 And now i'm leveled with the point.

02:13 So that means that my y coordinate is going to be positive 2 because we moved up.

02:21 So now we can focus on our problem...

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