Question Video: Writing Ordered Pairs for Points Plotted on Graphs Mathematics

Video Transcript

Write the ordered pair for the location of the monkeys.

We’re given a graph containing some points in a coordinate plane where the 𝑥-axis is horizontal and is perpendicular to the 𝑦-axis. The unit lengths are the same in the 𝑥- and 𝑦-directions; that is, one unit in the horizontal direction has the same length as one unit in the vertical direction. This coordinate plane is therefore an orthonormal coordinate plane.

That’s a plane 𝑂; 𝐼, 𝐽, where 𝑂 is the origin, the line through 𝑂 and 𝐼 represents the 𝑥-axis, the line through 𝑂 and 𝐽 represents the 𝑦-axis. 𝑂𝐼 is perpendicular to 𝑂𝐽. So, the axes are perpendicular, and the unit lengths 𝑂𝐼 and 𝑂𝐽 are equal. And we see that in the given graph, our coordinate plane has unit length, that’s 𝑂𝐼, equal to 𝑂𝐽, and that’s equal to one. So, our plane is an orthonormal coordinate plane.

Now, the position of any point 𝑀 in a coordinate plane 𝑂; 𝐼, 𝐽 is specified by the ordered pair 𝑥 sub 𝑀, 𝑦 sub 𝑀. And that’s where 𝑥 sub 𝑀 is the real number on the 𝑥-axis at the point of intersection of the line parallel to the 𝑦-axis and through 𝑀, and 𝑦 sub 𝑀 is the real number on the 𝑦-axis at the point of intersection of the line parallel to the 𝑥-axis and also through 𝑀.

Now, we’re asked to write the ordered pair for the location of the monkeys, that is, the coordinates of the position of the monkeys in the coordinate plane. And we see that the line through the location of the monkeys parallel to the 𝑦-axis goes through the number four on the 𝑥-axis so that 𝑥 sub 𝑀 is equal to four. Similarly, the line through monkeys parallel to the 𝑥-axis goes through the number five on the 𝑦-axis. And this means that 𝑦 sub 𝑀 is equal to five.

The ordered pair for the location of monkeys is, therefore, four, five.