Geometry Unit 1 Review

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).

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.

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).

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.

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).

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).

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).

Front

What is the formula for finding the point that partitions a segment in a given ratio on a number line?

Back

The formula is: P = \frac{n \cdot x_2 + m \cdot x_1}{m+n}, where m:n is the ratio and x_1, x_2 are the coordinates of points M and P.

Front

If point M is at 2 and point P is at 10, what point partitions M and P in the ratio 3:5?

Back

P = \frac{5 \cdot 2 + 3 \cdot 10}{3+5} = \frac{66}{8} = 8.25.

Front

What does it mean for a point to be 'fastened' at a specific location on a beam in geometry?

Back

It means that the point is fixed or secured at that location, which can be determined by partitioning the beam's length.