COORDINATE GEOMETRY - True/False

The distance between two points on the x-axis is the difference of their x-coordinates.

The distance between \((x_1,y_1)\) and \((x_2,y_2)\) in the plane is given by \((x_2-x_1)^2+(y_2-y_1)^2\).

If the distance between two distinct points in a plane is zero, then they are collinear.

The midpoint of the line segment joining \((x_1,y_1)\) and \((x_2,y_2)\) is \(\left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right)\).

Any point on the y-axis has coordinates of the form (x,0)(x,0).

A point in the second quadrant has positive x-coordinate and negative y-coordinate.

If a point divides a line segment internally in the ratio\( m_1:m_2\), the x-coordinate is \(\frac{m_1x_2+m_2x_1}{m_1+m_2}\).

The section formula can only be used for internal division of a line segment.

If the coordinates of the endpoints of a segment are known, its midpoint always lies between them on the same line.

Three points form a triangle of non-zero area if and only if they are collinear.

If the area of a triangle with vertices \((x_1,y_1),(x_2,y_2),(x_3,y_3)\) is zero, then the three points are collinear.

The formula for the area of a triangle with vertices \((x_1,y_1),(x_2,y_2),(x_3,y_3)\) involves only the x-coordinates of the vertices.

If two vertices of a triangle are fixed and the third vertex moves along a line parallel to the segment joining the fixed vertices, the area of the triangle remains constant.

For a line segment, if a point divides it in the ratio 1:1, the point is the midpoint of the segment.

If \((x_1,y_1)\) and \((x_2,y_2)\) are symmetric about the y-axis, then \(x_2=-x1\) and \(y_2=y_1\).

A point in the first quadrant always has a negative y-coordinate.

If a point lies on the x-axis, its ordinate is zero.

The distance formula in coordinate geometry is derived from the Pythagoras theorem.

If two points have the same x-coordinate, the line joining them is parallel to the x-axis.

The coordinates of any point on the line segment joining \((x_1,y_1\) and \((x_2,y_2)\) can be expressed using the section formula for some positive ratio.

In the coordinate plane, the origin is the point where the graph of every line passes.

If the area of a triangle formed by three points is zero, at least two points must coincide.

The coordinates of the centroid of a triangle with vertices \((x_1,y_1),(x_2,y_2),(x_3,y_3)\) is \(\left(\frac{(x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)\).

In coordinate geometry, the abscissa of a point is its y-coordinate.

If a point lies in the third quadrant, both its coordinates are negative.