Applications of Distance Formula

The video tutorial covers the application of the distance formula in a 3D coordinate system. It explains how to determine if points are collinear, form a right-angled triangle, square, rhombus, or parallelogram. The tutorial also demonstrates finding points on axes and planes that are equidistant from given points, and deriving equations for loci of points.

What is the formula used to determine if three points are collinear in a 3D space?

• Ratio of distances between two pairs of points equals the third distance

• Difference of distances between two pairs of points equals the third distance

• Product of distances between two pairs of points equals the third distance

• Sum of distances between two pairs of points equals the third distance

How can you verify if three points form a right-angled triangle using the distance formula?

• Check if the sum of the squares of two sides equals the square of the third side

• Check if the product of the distances equals zero

• Check if the sum of the distances equals zero

• Check if the sum of the distances equals the perimeter

What condition must be met for four points to be the vertices of a square?

• All sides and diagonals must be equal

• All sides must be equal but diagonals unequal

• Opposite sides must be equal and diagonals unequal

• All sides must be unequal

Which of the following is true for a rhombus in terms of side and diagonal lengths?

• All sides are equal and diagonals are unequal

• Opposite sides are equal and diagonals are equal

• All sides are unequal

• All sides and diagonals are equal

How do you determine a point on the Y-axis that is a specific distance from another point?

• Set X and Z coordinates to zero and solve for Y

• Set Y and Z coordinates to zero and solve for X

• Set X and Y coordinates to zero and solve for Z

• Set all coordinates to zero

What is the method to find a point on the X-axis equidistant from two given points?

• Set X and Y coordinates to zero and solve for Z

• Set all coordinates to zero

• Set X and Z coordinates to zero and solve for Y

• Set Y and Z coordinates to zero and solve for X

How do you find a point in the XY plane equidistant from two points?

• Set all coordinates to zero

• Set Y coordinate to zero and solve for X and Z

• Set X coordinate to zero and solve for Y and Z

• Set Z coordinate to zero and solve for X and Y

What is the process to find a point equidistant from four given points?

• Add distances from the point to each of the four points

• Equate distances from the point to each of the four points

• Subtract distances from the point to each of the four points

• Multiply distances from the point to each of the four points

How do you derive the equation of a locus of points a fixed distance from a given point?

• Use the distance formula and simplify

• Use the midpoint formula and simplify

• Use the slope formula and simplify

• Use the area formula and simplify

What is the method to find the equation of points equidistant from two given points?

• Use the area formula, equate, and simplify

• Use the slope formula, equate, and simplify

• Use the midpoint formula, equate, and simplify

• Use the distance formula, equate, and simplify