
Geometry Unit 1 Review

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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14 questions
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1.
FLASHCARD QUESTION
Front
What is the formula to find the coordinates of a point P that partitions a line segment AB in the ratio m:n?
Back
The coordinates of point P can be found using the formula: P = \left( \frac{m \cdot x_2 + n \cdot x_1}{m+n}, \frac{m \cdot y_2 + n \cdot y_1}{m+n} \right), where A(x_1, y_1) and B(x_2, y_2).
2.
FLASHCARD QUESTION
Front
Define the term 'partition' in the context of geometry.
Back
In geometry, 'partition' refers to dividing a line segment into parts in a specific ratio, determining the location of a point along the segment.
3.
FLASHCARD QUESTION
Front
Given points A(-14,8) and B(16,-2), find the coordinates of point P that partitions AB in the ratio 3:2.
Back
P = \left( \frac{3 \cdot 16 + 2 \cdot (-14)}{3+2}, \frac{3 \cdot (-2) + 2 \cdot 8}{3+2} \right) = (4, 2).
4.
FLASHCARD QUESTION
Front
What is the significance of the ratio in partitioning a line segment?
Back
The ratio indicates how the segment is divided, determining the relative distances from the endpoints to the partition point.
5.
FLASHCARD QUESTION
Front
If a line segment AB is divided in the ratio 1:3, how do you find the coordinates of the point of division?
Back
Use the formula: P = \left( \frac{1 \cdot x_2 + 3 \cdot x_1}{1+3}, \frac{1 \cdot y_2 + 3 \cdot y_1}{1+3} \right).
6.
FLASHCARD QUESTION
Front
What are the coordinates of point P that partitions the segment with endpoints A(-8,4) and B(16,-2) in the ratio 1:3?
Back
P = \left( \frac{1 \cdot 16 + 3 \cdot (-8)}{1+3}, \frac{1 \cdot (-2) + 3 \cdot 4}{1+3} \right) = (-2, 2.5).
7.
FLASHCARD QUESTION
Front
Explain how to express a point that partitions two points M and P in the ratio 7:9 on a number line.
Back
The expression is: \frac{9}{16}(point\ M) + \frac{7}{16}(point\ P).
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