Distance and Line Equations

This video tutorial explains how to calculate the perpendicular distance between a point and a line in both two and three dimensions. It introduces the formula for distance calculation and provides step-by-step examples for both 2D and 3D scenarios, demonstrating how to rearrange equations into standard form and apply the distance formula.

What is the formula to calculate the perpendicular distance from a point to a line in two dimensions?

• d = |ax + by + cz| / sqrt(a^2 + b^2)

• d = |ax1 + by1 + cz1 + d| / sqrt(a^2 + b^2 + c^2)

• d = |ax1 + by1 + c| / sqrt(a^2 + b^2)

• d = |ax1 + by1| / sqrt(a^2 + b^2)

In the first example, what are the values of a, b, and c for the line equation 3x - 4y + 18 = 0?

• a = 3, b = -4, c = -18

• a = -3, b = 4, c = 18

• a = 3, b = 4, c = -18

• a = 3, b = -4, c = 18

What is the distance between the point (4, 5) and the line 3x - 4y + 18 = 0?

• 2 units

• 1 unit

• 3 units

• 4 units

How do you rearrange the equation y = 5x/12 + 1/3 into standard form?

• 5x - 12y + 4 = 0

• 12x - 5y + 3 = 0

• -5/12x + y - 1/3 = 0

• 5x + 12y - 4 = 0

What is the distance between the point (3, -6) and the line y = 5x/12 + 1/3?

• 7 units

• 5 units

• 4 units

• 6 units

What is the first step in rearranging a line equation to standard form?

• Divide by the highest coefficient

• Add fractions to both sides

• Multiply by the reciprocal of the coefficients

• Move all terms to one side of the equation

In the third example, what are the values of a, b, c, and d for the line equation after rearrangement?

• a = 3, b = -6, c = -2, d = 12

• a = 3, b = 6, c = 2, d = -12

• a = -3, b = 6, c = -2, d = 12

• a = 3, b = -6, c = 2, d = -12

What is the distance between the point (2, 3, -4) and the line in the third example?

• 6 units

• 5 units

• 4 units

• 3 units

What is the purpose of multiplying by a common denominator when rearranging equations?

• To find the slope

• To balance the equation

• To simplify the equation

• To eliminate fractions

What is the final step in calculating the distance between a point and a line?

• Add the absolute value to the square root of the sum of squares

• Multiply the absolute value by the square root of the sum of squares

• Subtract the absolute value from the square root of the sum of squares

• Divide the absolute value by the square root of the sum of squares