Coordinate Geometry

Based on the diagram, which point has an ordinate of $0$?

Identify the abscissa of the point $L(7, -3)$.

If we move 3 units right and 4 units down from the origin, where do we land?

What is the ordinate of the point $K(-2, 6)$ shown in the diagram?

A rhombus is plotted with vertices $A(0,3)$, $B(4,0)$, $C(0,-3)$, and $D(-4,0)$. What is the length of diagonal $AC$?

The point $M$ is the midpoint of the segment $PQ$. If $P$ is $(1, 2)$ and $M$ is $(3, 2)$, what are the coordinates of $Q$?

What is the reflection of the point $H(-4, -6)$ in the origin?

A linear path is represented by the equation $y = x + 2$. A treasure is hidden at a point $T$ on this path such that its x-coordinate and y-coordinate are the same as the coordinates of the midpoint of the segment joining $(0, 4)$ and $(4, 0)$. Does the treasure lie on the path?

An isosceles triangle $ABC$ has its base $BC$ on the x-axis. The coordinates of $B$ are $(-2, 0)$ and $C$ are $(4, 0)$. If the altitude of the triangle is 5 units, find the coordinates of the vertex $A$ (assuming it is in the first quadrant).

A circle is drawn with its center at $C(2, 2)$. If the circle passes through the point $P(2, 6)$, which of the following points also lies on the circle?

In the given coordinate plane, a point $P$ is located at $(3, 4)$. What is the distance of point $P$ from the origin $O(0, 0)$?

Which of the following points is at a distance of 13 units from the origin?

What is the distance between points $A(-1, -1)$ and $B(2, 3)$?

The distance between $C(k, 0)$ and $D(0, 3)$ is 5 units. Find the positive value of $k$.

A point $C$ lies on the y-axis and is equidistant from $A(-4, 3)$ and $B(5, 2)$. What are the coordinates of point $C$?

Consider the triangle formed by the points $L(1, 2)$, $M(4, 2)$, and $N(4, 6)$ as shown in the diagram. Calculate the perimeter of triangle $LMN$.

A line segment $AB$ has its endpoints at $A(-2, 3)$ and $B(x, -1)$. If the length of the segment $AB$ is $5$ units, and $x$ is a positive integer, find the value of $x$.

The perimeter of an equilateral triangle is $3\sqrt{2}$ units. If two of its vertices are $(0, 0)$ and $(1, 1)$, what is the distance of the third vertex from the origin?

If the point $P(x, y)$ is at a distance of 5 units from the origin and its ordinate is double its abscissa, find the positive value of $x$.

A square has two opposite vertices at $(-1, 2)$ and $(3, 2)$. Find the area of the square.

A point $P$ divides the line segment joining $X(1, 3)$ and $Y(4, 6)$ internally in the ratio $2:1$. Using the section formula, determine the coordinates of $P$.

In the given figure, point $M$ is the mid-point of the line segment joining the points $A(-4, 6)$ and $B(2, -2)$. Find the coordinates of point $M$.

Point $M$ is the midpoint of segment $AB$. If $A = (2, 3)$ and $M = (5, 7)$, find the coordinates of $B$.

The coordinates of the mid-point of the segment $AB$ are $(1, 2)$. If $A$ is $(-2, 2)$, find $B$.

Find the length of the median through $A$ of $\triangle ABC$ with $A(2, 2)$, $B(6, -1)$ and $C(7, 3)$.

Find the point $P$ on the x-axis which is equidistant from $A(2, -5)$ and $B(-2, 9)$.

If $G(4, 3)$ is the centroid of $\triangle ABC$ where $A(x, 2)$, $B(5, y)$ and $C(-1, 4)$, find $x$ and $y$.

A circle has its center at $C(4, 4)$ and passes through the point $P(7, 8)$. If $PQ$ is a diameter of the circle, calculate the coordinates of point $Q$.

The line segment joining $A(3, 2)$ and $B(5, 1)$ is divided by the line $3x - 2y = 12$ in the ratio $m:n$. Find this ratio.

Point $C(-1, 2)$ divides the line segment joining $A(2, 5)$ and $B(x, y)$ externally in the ratio $3 : 4$. Find the coordinates of $B$.