Question

Which of the following statements is true for a point in the first quadrant of the coordinate plane?

A. To graph a point (x, y) in the first quadrant of the coordinate plane, move x units up from the origin and y units to the left.

B. To grab a point (x, y) in the first quadrant of the coordinate plane, move x units to the right of the origin and y units up.

C. To graph a point (x, y) in the first quadrant of the coordinate plane, move x units to the left of the origin and y units up.

C. To graph a point (x, y) in the first quadrant of the coordinate plane, move x units from the origins and Y units to the right.

D. To graph a point (x, y) in the first quadrant of the coordinate plane, move x units up from the origin and y units to the right.

Answer 1

Choice B: Start at the origin. Move
`x` units to the right, and
`y` units upwards.

Explanation:

There are two axes on a typical Cartesian coordinate plane:

• The horizontal
  `x`-axis, and
• The vertical
  `y`-axis.

Many diagrams of a Cartesian plane would have arrows on these two axis. Typically, there would be:

• a rightward arrow
  `\verb!->!` on the right-hand side of the horizontal
  `x`-axis, and
• an upward arrow
  `\uparrow` at top of the vertical
  `y`-axis.

The arrow on the
`x`-axis pointing rightward suggests that as a point move to the right, the
`x\!` coordinate of that point would increase. Conversely, it would be necessary to move points to the right so as to increase their
`\! x`-coordinates.

On the other hand, the arrow pointing upwards on the
`y`-axis indicate that as a point move upward, the
`y\!` coordinate of that point would increase. With a similar logic, it would be necessary to move points upward to increase their
`\! y`-coordinates.

Besides, the origin (the intersection of the two axis, unless otherwise specified) would corresponds to
`(0,\, 0)`. (That is:
`x = 0` and
`y = 0`.) If the origin
`(0,\, 0)\!` is the starting point, it would be necessary to increase the
`x`-coordinate by
`x\!` units (by moving rightward
`x\!\!` units) and increase the the
`y`-coordinate by
`y\!` units (by moving upwards
`y\!\!` units) so as to reach the point
`(x,\, y)`.