Measuring line segments

Front

What is the formula for finding the length of a line segment between two points A(x1, y1) and B(x2, y2)?

Back

The length of the line segment AB is given by the formula: \( AB = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \)

Front

If AB = 2x + 3 and AC = 38, how do you find the value of x?

Back

Set up the equation: AB + BC = AC. Substitute AB and solve for x.

Front

What does it mean for line segments AB and BC to be equal?

Back

It means that the lengths of the segments AB and BC are the same.

Front

How do you solve for x in the equation 3x - 5 = 11?

Back

Add 5 to both sides to get 3x = 16, then divide by 3 to find x.

Front

What is the distance between points (4, -12) and (4, 0)?

Back

The distance is 12 units, calculated as |y2 - y1| = |0 - (-12)|.

Front

If the length of segment AB is 20 and BC is 19, what is the length of AC?

Back

AC = AB + BC = 20 + 19 = 39.

Front

What is the significance of a negative length in a line segment?

Back

A negative length indicates an error in measurement or calculation, as lengths cannot be negative.

Front

How do you plot the point (4, -12) on a coordinate plane?

Back

Start at the origin (0,0), move right 4 units, and then down 12 units.

Front

What is the relationship between the lengths of line segments in a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side (Triangle Inequality Theorem).

Front

If AB = 2x + 3 and BC = 3x - 5, how do you find the value of x when AC = 38?

Back

Set up the equation: (2x + 3) + (3x - 5) = 38 and solve for x.