Question

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

Answer 1

Answer:

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

Step-by-step 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 $(x,\, y)$.