What is the relationship between the point (4,7) and the vector (4,7)? Illustrate with a sketch.
The point(4,7), means when X - 4, Y = 7.
The vector (4,7) represents 2 lines: The first drawn 4 units to the right of 0
with head (arrow) pointed to the right.. The tail of the second connects to the head of the first and points upward 7 units.
Ah, the relationship between a point and a vector! Well, you see, a point is like a little dot on a map, just hanging out, while a vector is like a fancy arrow, showing direction and magnitude. So, the point (4,7) is just a specific location on the coordinate plane, like a little pin on a map. Meanwhile, the vector (4,7) is like an arrow starting from the origin (0,0) and ending at the point (4,7), indicating how to get there.
Now, let's picture this. Imagine a blank canvas, and on it, draw a point at the coordinates (4,7). It's just a little dot, chilling out all by itself. Then, draw an arrow starting from the origin (0,0) and extending to the point (4,7). This arrow represents the vector (4,7). It's pointing towards our little dot, showing us the direction and magnitude of getting from the origin to that point.
So, to sum it up, the point (4,7) is a specific location, while the vector (4,7) is an arrow starting from the origin and pointing towards that location.
The point (4,7) and the vector (4,7) have a strong relationship because they have the same values. In this case, both the point and the vector have x=4 and y=7.
To illustrate this relationship with a sketch, we can imagine a coordinate plane.
First, let's mark the point (4,7) on the coordinate plane as a dot. This point represents a specific location in the plane.
Next, let's draw a vector starting from the origin (0,0) and ending at the point (4,7). This vector is represented by an arrow that points from the origin to the point (4,7). Since the vector (4,7) has the same values as the point (4,7), the arrow will have the same length and direction as the line segment connecting the origin to the point (4,7).
By sketching the point (4,7) and the vector (4,7), we can visually understand their relationship: the vector represents a magnitude and direction from the origin to the point, while the point represents a specific location in the plane.
The relationship between a point and a vector is that a point represents a position in space, while a vector represents a direction and magnitude. Let's illustrate this with a sketch.
To begin, visualize a coordinate system with the x and y axes. The point (4,7) represents a specific location on this coordinate system. It is located 4 units to the right on the x-axis and 7 units upwards on the y-axis.
On the other hand, the vector (4,7) represents a direction and magnitude that can be interpreted as a movement. Starting from the origin (0,0), you can imagine moving 4 units to the right on the x-axis and 7 units upwards on the y-axis, following the direction indicated by the vector.
In summary, the point (4,7) represents a location in space, whereas the vector (4,7) represents a direction and magnitude that can be used to describe a movement from the origin to (4,7).