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Questions and Answers
What does the formula for the internal division point P(x, y) represent?
What does the formula for the internal division point P(x, y) represent?
- A midpoint of a line segment
- A point where two lines intersect
- A point dividing a segment internally (correct)
- A point dividing a segment externally
What is the correct formulation for the y-coordinate in the internal division formula?
What is the correct formulation for the y-coordinate in the internal division formula?
- y = (y1 + y2) / 2
- y = m1(y2 - y1) / (m2 + m1)
- y = (m1y2 + m2y1) / (m1 + m2) (correct)
- y = m1y2 + m2y1 / m1 - m2
In the formula P(x, y) = (m1x2 + m2x1) / (m1 + m2), what do m1 and m2 represent?
In the formula P(x, y) = (m1x2 + m2x1) / (m1 + m2), what do m1 and m2 represent?
- The distances from point P to x1 and x2
- The weights for division on the x-coordinate (correct)
- The coordinates of point P
- The lengths of segments created by point P
If m1 = 2 and m2 = 3, what is the total weight used for the internal division formula?
If m1 = 2 and m2 = 3, what is the total weight used for the internal division formula?
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Which of the following expressions correctly represents the x-coordinate in the internal division formula?
Which of the following expressions correctly represents the x-coordinate in the internal division formula?
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Study Notes
Internal Division Point Formula
- The internal division point formula calculates the coordinates of a point that divides a line segment internally in a given ratio.
- P(x, y) = (m1x2 + m2x1) / (m1 + m2), (m1y2 + m2y1) / (m1 + m2) is the formula used for the internal division point.
- The y-coordinate of the internal division point is (m1y2 + m2y1) / (m1 + m2)
- m1 and m2 represent weights or ratios, determining how the line segment is divided.
- The total weight used in the formula is the sum of the weights, m1 + m2.
- If m1 = 2 and m2 = 3, the total weight is 5.
- (m1x2 + m2x1) / (m1 + m2) correctly represents the x-coordinate in the internal division formula.
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