Coordinate Geometry Maths - Coordinate Geometry

The disrtance of point P(2, 3) from the X-axis is:

A line intersects the y-axis and X-axis at the points P and Q, respectively. If (2, – 5) is the mid-point of PQ, then the coordinates of P and Q are, respectively:

State whether the following statements are true or false. Justify your answer.
Points A(4, 3), B(6, 4), C(5, -6) and D(-3, 5) are the vertices of a parallelogram.

State whether the following statements are true or false. Justify your answer.
The points (0, 5), (0, -9) and (3, 6) are collinear.

State whether the following statements are true or false. Justify your answer.
The points A(-1, -2), B(4, 3), C(2, 5) and D(-3, 0) in that order form a rectangle.

State whether the following statements are true or false. Justify your answer.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.

Find the value of m if the points (5, 1), (-2, -3) and (8, 2m ) are collinear.

The line segment joining the points A (3, 2) and B (5, 1) is divided at the point P in the ratio 1 : 2 and it lies on the line 3x - 18y + k = 0. Find the value of k.

If the point A(2, -4) is equidistant from P(3, 8) and Q(-10, y), find the values of y. Also find distance PQ.

Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.