NO LINKS!! Describe the set of all points P(x, y) in a coordinate plane that satisfy the given condition. Part 2
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Part (d)
If xy > 0, then the two items x and y must have the same sign.
Examples where x,y are both positive
Examples where x,y are both negative
This places us in either the first quadrant or third quadrant (Q1 and Q3)
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Part (e)
If y < 0, then we have points like (2,-5) and (1,-7). The x coordinate doesn't matter as long as the y coordinate is negative.
Visually speaking we are below the x axis. This places the point in Q3, Q4, or on the negative y axis. The point cannot be on the x axis. You can think of this point as being underground or underwater.
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Part (f)
If x = 0, then the point is on the vertical y axis. Recall that y intercepts always occur when x = 0. Two examples would be (0,4) and (0,12).
Answer:
(d) The set of all points in quadrants I and III (x and y have the same sign).
(e) The set of all points below the x-axis.
(f) The set of all points on the y-axis.
Step-by-step explanation:
The Cartesian plane is divided into four quadrants.
Quadrant I is the upper right quadrant and the rest follow in a counterclockwise direction.
Part (d)
For xy > 0, x and y should either both be positive or both be negative, i.e. have the same sign.
Therefore, the description that satisfies the given condition is:
Part (e)
For y < 0, y is always negative.
Quadrants III and IV are below the x-axis.
Therefore, the description that satisfies the given condition is:
Part (f)
The only place where x = 0 is the y-axis.
Therefore, the description that satisfies the given condition is: