Here are two identical shaded triangles on coordinate axes. Write the coordinates of points 𝐴 and 𝐵.
The question is asking us to find the coordinates of the points 𝐴 and 𝐵. We know the triangles are identical. So the length between the two points I’ve marked in blue is also identical. Because we’re looking for the length of this line, we’re looking at the coordinates on the 𝑥-axis, how far along the 𝑥-axis this line goes.
If we look closely at these coordinates, we can see that the first point is zero on the 𝑥-axis and the second point is three on the 𝑥-axis, which gives us a difference of three. The same is true of the line on the second triangle. The distance between these two points has a difference of three on the 𝑥-axis. Nine plus three is 12. We haven’t changed the 𝑦-coordinate so that stays as zero. The coordinates for point 𝐴 are 12, zero.
Now we need to find the coordinates for point 𝐵. The coordinates of this point on the first triangle are not given. But if we look closely and think about this, we can see that this point is at zero, zero. Now we can see that the 𝑦-coordinate of this point has changed from eight to zero, which is a difference of eight. So the 𝑦-coordinate of point 𝐵 will be eight less than zero, which is negative eight or minus eight. And the position of the 𝑥-coordinate stays the same.
The coordinates of point 𝐴 are 12, zero. And the coordinates of point 𝐵 are nine, negative eight.