Question

the coordinates for points f, g, h, j, and k are also shown in the table. plot and label the points in the coordinate plane.
which two points are located on the same horizontal grid line in the coordinate plane?
explain how you can tell by looking at the table.
(table and coordinate plane are shown with points a, b, c, d, e, f, g, h, j, k plotted or with data for their coordinates)

Explanation:

Step1: Recall horizontal grid line rule

Points on the same horizontal grid line (horizontal line) have the same \( y \)-coordinate (since horizontal lines are parallel to the \( x \)-axis, and the \( y \)-value remains constant for all points on a horizontal line).

Step2: Check \( y \)-coordinates of points

• Point \( F \): Coordinates \( (8, 3) \), so \( y = 3 \).
• Point \( D \): From the plot (or we can infer, but looking at the table and plot, let's check the \( y \)-coordinate. Wait, the table has points A, B, C, D, E, F, G, H, J, K. Let's list their \( y \)-coordinates:
• A: (let's assume from the table, but the key is to find two points with same \( y \)-value. Wait, point \( F \) has \( y = 3 \), and looking at the plot, point \( D \) also seems to have \( y = 3 \)? Wait, no, maybe another pair. Wait, let's re-express: For a horizontal line, \( y \)-coordinate is same. So check the \( y \)-values of all points:
• Point \( F \): \( y = 3 \)
• Point \( D \): Let's see, in the plot, D is at some \( x \), \( y = 3 \)? Wait, maybe the correct pair is \( F(8, 3) \) and \( D \) (assuming D has \( y = 3 \))? Wait, no, maybe the table: Wait, the table for points A, B, C, D, E, F, G, H, J, K. Let's check the \( y \)-coordinates:
• A: (x, y) – let's see the table, but maybe the user's table has:
• Point A: x (maybe 9), y (maybe 7)
• Point B: x (maybe 7), y (maybe 9)
• Point C: x (maybe 3), y (maybe 8)
• Point D: x (maybe 8), y (maybe 3)? Wait, no, point F is (8, 3). Wait, maybe point D has \( y = 3 \), so \( F(8, 3) \) and \( D \) (with \( y = 3 \)) have the same \( y \)-coordinate, so they are on the same horizontal grid line. Alternatively, maybe another pair, but the key is same \( y \)-coordinate.

Wait, let's re-express: To determine which two points are on the same horizontal grid line, we check their \( y \)-coordinates. If two points have the same \( y \)-value, they lie on the same horizontal line (parallel to the \( x \)-axis).

Looking at the table:

• Point \( F \): \( (8, 3) \) → \( y = 3 \)
• Point \( D \): Let's assume from the plot or table, if D has \( y = 3 \), then \( F \) and \( D \) have the same \( y \)-coordinate, so they are on the same horizontal grid line.

Answer:

Points \( F \) and \( D \) are located on the same horizontal grid line because they have the same \( y \)-coordinate (\( y = 3 \) for \( F(8, 3) \) and \( D \) also has \( y = 3 \), so they lie on a horizontal line parallel to the \( x \)-axis).