Practice Coordinate Geometry MCQs with Detailed Solutions – Level 3

A point P on the x-axis is equidistant from A(2, −5) and B(−2, 9). What are the coordinates of P?

In what ratio does the y-axis divide the line segment joining (−4, 6) and (8, −3), and what is the point of division?

Two vertices of a triangle are (3, −5) and (−7, 4). If its centroid is (2, −1), what is the third vertex?

The area of the triangle with vertices (2, 3), (−1, 0) and (k, −4) is 15 square units. What is the sum of all possible values of \(k?\)

The line through the points (3, k) and (k, 5) is perpendicular to the line \(2x - 3y + 7 = 0.\) What is the value of \(k?\)

A line not passing through the origin passes through (2, −3). Its x-intercept and y-intercept are equal in magnitude but opposite in sign. What is its equation?

The sum of the x-intercept and the y-intercept of the line \(3x - 5y = k\) is 8. What is the value of \(k?\)

The segment of a line intercepted between the coordinate axes is bisected at the point (4, 3). What is the area of the triangle formed by this line with the coordinate axes?

What is the equation of the line through (−2, 5) that is perpendicular to the line joining (1, 3) and (4, −3)?

The points (0, 1), (k, 3) and (6, k) are collinear. What are the possible values of \(k?\)