Orienting Yourself: The Use of Coordinates

A point $P$ is located in the Cartesian plane as shown. What are the coordinates of point $P$ based on its distances from the axes?

The point $M(-4, 0)$ lies on which part of the coordinate system?

Points $A(1, 2)$ and $B(1, -5)$ lie on a line parallel to the:

The vertical line in a Cartesian plane is called the:

A triangle is formed by the points $X(0,4)$, $Y(0,0)$, and $Z(3,0)$. What is the area of this triangle?

Observe the line segment $PQ$ in the diagram. If point $M$ is the midpoint of $PQ$, what are the coordinates of $M$?

A square $ABCD$ is positioned such that its center is at the origin $(0,0)$ and its sides are parallel to the axes. If the coordinate of vertex $A$ is $(2,2)$, find the coordinates of vertex $C$, which is diagonally opposite to $A$.

A line segment $GH$ is drawn such that $G$ is at $(0, 4)$ and $H$ is at $(0, -2)$. A point $I$ is placed on the positive x-axis such that the area of triangle $GHI$ is 15 square units. What are the coordinates of point $I$?

A point $M$ is located 5 units from the x-axis and 3 units from the y-axis. If $M$ lies in the second quadrant, find the coordinates of the point $N$ which is the reflection of $M$ in the x-axis.

Consider the points $A(1, 2)$, $B(3, 2)$, and $C(1, 5)$. If these points are the vertices of a right-angled triangle, find the length of the hypotenuse $BC$.

A point $P$ is located on the Cartesian plane as shown in the diagram below. What are the coordinates of point $P$?

Identify the point with coordinates $(-2, 4)$ from the options plotted.

Which axis is the line shown in the diagram parallel to?

In the diagram, what is the distance of point $C$ from the y-axis?

The distance of a point from the x-axis is $3$ units and from the y-axis is $5$ units. If the point lies in the fourth quadrant, its coordinates are:

Determine the coordinates of the point that is the reflection of $(-4, -1)$ in the y-axis.

If $P(a, b)$ is a point in the third quadrant, which of the following is true?

In a game of battleship, a cruiser occupies four consecutive grid intersections. Three of the points are $(2, 2)$, $(2, 3)$, and $(2, 4)$. Which of the following could be the fourth point if the cruiser forms a straight vertical line?

An equilateral triangle $ABC$ has vertex $A$ at $(0, 4)$ and vertex $B$ at $(0, -4)$. If vertex $C$ lies on the positive x-axis, find the coordinates of $C$. (Hint: use the distance formula or properties of $30-60-90$ triangles)

A point $M$ is reflected across the x-axis to $M'(3, -4)$. Then $M'$ is reflected across the y-axis to $M''$. What are the coordinates of $M''$?

The coordinates of a point $M$ are $(-2, 0)$. In which direction from the origin is it located?

If the y-coordinate of a point is zero, then this point always lies:

Any point on the line $y = 0$ is of the form:

Points where the abscissa and ordinate have opposite signs (excluding zeros) lie in which quadrants?

A rectangle $ABCD$ is plotted in the Cartesian plane as shown in the diagram. If the coordinates of $A$ are $(-3, 2)$ and $B$ are $(4, 2)$, and the length of the side $BC$ is $5$ units, find the coordinates of the vertex $D$ given that it lies in the third quadrant.

Point $Q$ is the reflection of point $P(2, -3)$ across the x-axis. What are the coordinates of point $Q$?

A triangle $OAB$ has its vertices at $O(0, 0)$, $A(6, 0)$, and $B(0, 8)$. What is the length of the side $AB$?

The vertices of a triangle are $A(0, 0)$, $B(4, 0)$, and $C(0, 3)$. This triangle is rotated $180^{\circ}$ about the origin. What are the new coordinates of vertex $C$?

A treasure is hidden at a point $T$ such that its distance from the x-axis is $5$ units and its distance from the y-axis is $3$ units. If $T$ lies in the third quadrant, find its coordinates.

The linear equation $y = x + 2$ represents a fence. A lamp post is located at $L(4, 2)$. If we want to find a point $F$ on the fence that has the same x-coordinate as the lamp post, what are the coordinates of $F$?

If a point $P$ lies on the x-axis at a distance of 7 units from the y-axis to the left of the origin, what is its coordinate?

What is the distance between the points $A(a, 0)$ and $B(0, a)$?

Find the distance between points $(2, 3)$ and $(2, -1)$.

In the figure, $O$ is the origin. What is the distance $OA$?

Point $C$ is the midpoint of the line segment joining $A(2, 4)$ and $B(6, 8)$. Find the distance $AC$.

Show that the points $(1, 7)$, $(4, 2)$, and $(-1, -1)$ are the vertices of a triangle. Find the length of the side joining $(1, 7)$ and $(-1, -1)$.

Find the distance between the points $A(x_1, y_1)$ and $B(x_2, y_2)$ if the segment $AB$ is parallel to the y-axis.

A point $P$ is at a distance of 5 units from the origin and lies in the second quadrant. If the ordinate (y-coordinate) of $P$ is twice its abscissa (x-coordinate) in absolute value, find the coordinates of $P$.

An equilateral triangle has two vertices at $(0, 0)$ and $(4, 0)$. Which of the following could be the third vertex?

A shipyard uses a coordinate system where a ship is at $S(7, 4)$. A lighthouse $L$ is at $(1, -4)$. A rescue boat must stop at a point $X$ on the x-axis that is part of the path minimizing the total distance $SX + XL$. While the reflection principle is complex, simply find the distance between $S$ and $L$.