Coordinate Geometry(Distance formula and Section formula)

Front

What is the distance formula in coordinate geometry?

Back

The distance formula is given by: d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of two points.

Front

How do you find the distance of a point from the x-axis?

Back

The distance of a point (x, y) from the x-axis is the absolute value of its y-coordinate, |y|.

Front

How do you find the distance of a point from the y-axis?

Back

The distance of a point (x, y) from the y-axis is the absolute value of its x-coordinate, |x|.

Front

What is the section formula in coordinate geometry?

Back

The section formula is used to find the coordinates of a point that divides a line segment in a given ratio. If point P divides the line segment joining points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of P are given by: P(x, y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).

Front

If M is the midpoint of a line segment joining points A(x1, y1) and B(x2, y2), what are the coordinates of M?

Back

The coordinates of the midpoint M are given by: M((x1 + x2)/2, (y1 + y2)/2).

Front

What is the significance of the x-axis in coordinate geometry?

Back

The x-axis is the horizontal line in a coordinate plane where y = 0. It is used as a reference line to determine the position of points.

Front

What is the significance of the y-axis in coordinate geometry?

Back

The y-axis is the vertical line in a coordinate plane where x = 0. It is used as a reference line to determine the position of points.

Front

How do you determine if a point lies on the x-axis?

Back

A point lies on the x-axis if its y-coordinate is 0.

Front

How do you determine if a point lies on the y-axis?

Back

A point lies on the y-axis if its x-coordinate is 0.

Front

What is the formula to calculate the distance between two points P(0, y) and Q(x, 0)?

Back

The distance between P(0, y) and Q(x, 0) is given by: d = √(x² + y²).