Question

NO LINKS!! Describe the set of all points P(x, y) in a coordinate plane that satisfy the given condition​

Answer 1

(a) The line parallel to the y-axis that intersects the x-axis at (-8, 0).

(b) The line parallel to the x-axis that intersects the y-axis at (0, 8).

(c) The set of all points to the right of and on the y-axis.

Explanation:

Part (a)

Given condition: x = -8

The equation of a vertical line is x = a.

This line is parallel to the y-axis (since it is vertical) and intersects the x-axis at (a, 0).

Therefore, the description that satisfies the given condition is:

• The line parallel to the y-axis that intersects the x-axis at (-8, 0).

Part (b)

Given condition: y = 8

The equation of a horizontal line is y = a.

This line is parallel to the x-axis (since it is horizontal) and intersects the y-axis at (0, a).

Therefore, the description that satisfies the given condition is:

• The line parallel to the x-axis that intersects the y-axis at (0, 8).

Part (c)

Given condition: x ≥ 0

The "≥" symbol means greater than or equal to.

x is greater than zero for all points to the right of the y-axis.

x is equal to zero for all points on the y-axis.

Therefore, the description that satisfies the given condition is:

• The set of all points to the right of and on the y-axis.

Answer 2

• a) A or first option,
• b) E or 5th option,
• c) E or 5th option.

Explanation:

a) x = - 8

Simply check for x-coordinate of - 8, we see only the first option has it, all the others have x = 0 or x = 8 which is impossible to have on the line x = - 8.

It is parallel to the y-axis and x = - 8 for any value of y.

Correct choice is A or 1.

b) y = 8

Similar to above, we exclude all the options with a different value of y other than 8.

There are two possible options left:

• B or 2- incorrect as y = 0 is parallel to the x-axis, not perpendicular.
• E or 5 - correct option

c) x ≥ 0

Consider line x = 0, this is overlapping with the y-axis.

x ≥ 0 gives us the y-axis (because of equal sign) and all the points to the right from it.

This is matching the description of option E or 5.