Question

Study the grid closely and name the ordered pairs of the 4 red points A, B, C, D on this coordinate system. Will the line joining A &

B pass through D? How would you prove that it does or does not? Answer in the discussion below!

Answer 1

9514 1404 393

Answer:

• A(0, 0), B(1, 1), C(5, 1), D(8, 7)
• no; Dx ≠ Dy

Explanation:

1) Upon studying the grid, we see that A is at the intersection of the x- and y-axes, and that all of the other points are in the first quadrant. The distance between minor grid lines in either direction is taken to be 1 unit. That is, B is 1 unit right and 1 unit up from A(0, 0), so has coordinates B(1, 1).

The coordinates of C and D can be found by counting grid lines. We find them to be C(5, 1) and D(8, 7).

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2) The line joining A and B is a line whose points have their x-coordinate equal to their y-coordinate. The coordinates of D are not equal, so will not be on that line.