The coordinates of the points that divide the line segment joining A(-2, 4) and B(2, 10) into four equal parts can be found as follows:
The midpoint of the line segment is given by the formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
Where M is the midpoint, (x1, y1) is the coordinate of point A, and (x2, y2) is the coordinate of point B.
Substituting the values (-2, 4) for (x1, y1) and (2, 10) for (x2, y2), we get:
M = ((-2 + 2)/2, (4 + 10)/2)
= (0, 7)
Thus, the midpoint of the line segment is (0, 7).
The coordinates of the points that divide the line segment into four equal parts can be found by considering the line segment as four smaller line segments, each of which is 1/4 the length of the original line segment.
The coordinates of the points that divide the line segment into four equal parts are given by the formula:
P1 = (x1 + 3(x2 - x1)/4, y1 + 3(y2 - y1)/4)
P2 = (x1 + (x2 - x1)/4, y1 + (y2 - y1)/4)
Where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively, and P1 and P2 are the coordinates of the points that divide the line segment into four equal parts.
Substituting the values (-2, 4) for (x1, y1) and (2, 10) for (x2, y2), we get:
P1 = (-2 + 3(2 - (-2))/4, 4 + 3(10 - 4)/4)
= (-2 + 3(4)/4, 4 + 3(6)/4)
= (-2 + 12/4, 4 + 18/4)
= (-2 + 3, 4 + 4.5)
= (1, 8.5)
P2 = (-2 + (2 - (-2))/4, 4 + (10 - 4)/4)
= (-2 + (4)/4, 4 + (6)/4)
= (-2 + 1, 4 + 1.5)
= (-1, 5.5)
Thus, the coordinates of the points that divide the line segment into four equal parts are (1, 8.5) and (-1, 5.5).
Answers & Comments
Answer:
The coordinates of the points that divide the line segment joining A(-2, 4) and B(2, 10) into four equal parts can be found as follows:
The midpoint of the line segment is given by the formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
Where M is the midpoint, (x1, y1) is the coordinate of point A, and (x2, y2) is the coordinate of point B.
Substituting the values (-2, 4) for (x1, y1) and (2, 10) for (x2, y2), we get:
M = ((-2 + 2)/2, (4 + 10)/2)
= (0, 7)
Thus, the midpoint of the line segment is (0, 7).
The coordinates of the points that divide the line segment into four equal parts can be found by considering the line segment as four smaller line segments, each of which is 1/4 the length of the original line segment.
The coordinates of the points that divide the line segment into four equal parts are given by the formula:
P1 = (x1 + 3(x2 - x1)/4, y1 + 3(y2 - y1)/4)
P2 = (x1 + (x2 - x1)/4, y1 + (y2 - y1)/4)
Where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively, and P1 and P2 are the coordinates of the points that divide the line segment into four equal parts.
Substituting the values (-2, 4) for (x1, y1) and (2, 10) for (x2, y2), we get:
P1 = (-2 + 3(2 - (-2))/4, 4 + 3(10 - 4)/4)
= (-2 + 3(4)/4, 4 + 3(6)/4)
= (-2 + 12/4, 4 + 18/4)
= (-2 + 3, 4 + 4.5)
= (1, 8.5)
P2 = (-2 + (2 - (-2))/4, 4 + (10 - 4)/4)
= (-2 + (4)/4, 4 + (6)/4)
= (-2 + 1, 4 + 1.5)
= (-1, 5.5)
Thus, the coordinates of the points that divide the line segment into four equal parts are (1, 8.5) and (-1, 5.5).
Step-by-step explanation:
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