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Segment AB has seven equally spaced points on it. Starting at A and moving left to right, the points are C, D, E, F, G, H, and I.
In the diagram,
is divided into equal parts. The coordinates of point A are (-3, 9), and the coordinates of point B are (9, 5).
The coordinates of point C are
.
The coordinates of point E are
.
The coordinates of point H are
.
The coordinates of point C are (-2, 8).
The coordinates of point E are (0, 7).
The coordinates of point H are (5, 6).
The coordinates of point C are (-2, 8).
The coordinates of point E are (0, 7).
The coordinates of point H are (6, 6).
To determine the coordinates of each point on segment AB, we'll need to find the distance between points A and B and divide it equally among the points.
First, let's find the distance between points A and B:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given that point A has coordinates (-3, 9) and point B has coordinates (9, 5), substituting the values into the distance formula, we have:
Distance = sqrt((9 - (-3))^2 + (5 - 9)^2)
Distance = sqrt((12)^2 + (-4)^2)
Distance = sqrt(144 + 16)
Distance = sqrt(160)
Distance = 12.65 (approx.)
Now, let's divide this distance equally among the 6 intervals between points A and B. To do this, we divide the total distance by 6:
Interval distance = 12.65 / 6
Interval distance = 2.11 (approx.)
To find the coordinates of each point on segment AB, we start with the coordinates of point A (-3, 9) and add the interval distance repeatedly until we reach point B (9, 5).
The coordinates of point C can be found by adding the interval distance twice to point A:
Point C = (x1 + 2 * interval distance, y1)
Point C = (-3 + 2 * 2.11, 9)
Point C = (-3 + 4.22, 9)
Point C = (1.22, 9)
Similarly, to find the coordinates of point E, we add the interval distance four times to point A:
Point E = (x1 + 4 * interval distance, y1)
Point E = (-3 + 4 * 2.11, 9)
Point E = (-3 + 8.44, 9)
Point E = (5.44, 9)
Finally, to find the coordinates of point H, we add the interval distance six times to point A:
Point H = (x1 + 6 * interval distance, y1)
Point H = (-3 + 6 * 2.11, 9)
Point H = (-3 + 12.66, 9)
Point H = (9.66, 9)
Therefore, the coordinates of point C are (1.22, 9), the coordinates of point E are (5.44, 9), and the coordinates of point H are (9.66, 9).