A coordinate system is used to determine the position of points in ___ and ___.

Space and mathematical frameworks

The distance between two points in a coordinate plane can be calculated using the ___ formula.

Distance

The coordinates of the midpoint M between points A(x₁, y₁) and B(x₂, y₂) are given by ___ and ___.

((x₁ + x₂) / 2, (y₁ + y₂) / 2)

The distance of point P(x, y) from the origin O(0, 0) is calculated as ___ .

√(x² + y²)

If a point divides a line segment in the ratio 2:3, the coordinates of that point can be found using the ___ formula.

Section

What is the abscissa of a point in a coordinate plane?

The distance of a point from the Y-axis

If point A is at (-1, -1) and point B is at (3, 3), the midpoint M is at ___ .

(1, 1)

The distance between the points (3, 4) and (7, 1) is calculated as ___ .

√[(7 - 3)² + (1 - 4)²] = √[16 + 9] = √25 = 5

If point P divides the line segment joining A(1, 2) and B(3, 4) internally in the ratio 1:1, the coordinates of point P are ___ .

(2, 3)

The coordinate of point P(5, -6) indicates that its distance from the X-axis is ___ and from the Y-axis is ___.

6 and 5

True or False: The formula for distance between two points is derived from Pythagoras' theorem.

True

Fill in the blank: The coordinates of the point that divides the line segment joining A(x₁, y₁) and B(x₂, y₂) in the ratio m:n are ___.

((mx₂ + nx₁) / (m + n), (my₂ + ny₁) / (m + n))

If the coordinates of point A are (2, -3) and point B are (-1, 5), what is the midpoint M?

(0.5, 1)

True or False: The ordinate of a point is the distance from the X-axis.

True

The distance formula can be represented as d = ___ .

√[(x₂ - x₁)² + (y₂ - y₁)²]

If the distance between points (0, 0) and (x, y) is 10, then ___ .

√(x² + y²) = 10