Find the equation of the straight line passing through the points (3, - 4) and (1, 2) and hence show that the three points (3 ,-4), (1, 2 ) and (2, - 1) are collinear.
Equation of a straight line --> Slope and Intercept or Slope and point
Collinear --> Distance Formula or Slope
If the point (h, -2) is collinear with the points (2, 2) and (-3, 1) then find the value of h.
Also, find the slope of the line containing the three points.
Which point on the y-axis is equidistance from the points (12, 3) and (-5, 10)?
Find the values of a such that PQ = QR, where P, Q and R are the points whose coordinates are (6, - 1), (1, 3) and (a, 8) respectively.
Find the point A’ if the point A (-3, 4) on reflection in the point (1, -1) maps onto the point A’.
Find the perpendicular distance between the line 4x - y = 5 and the point (2, - 1).
Find the equation of the straight line passing through the points (2, 3) and (6, - 5).
Find the co-ordinates of, the middle point of the portion of the line 5x + y = 10 intercepted between the x and y-axes.
Find the area of the triangle formed by the axes of co-ordinates and the straight line 5x + 7y = 35.
Without using the Pythagoras theorem, show that P (4, 4), Q (3, 5) and R (-1, -1) are the vertices of a right angled triangle.
Challenging:
Find the ortho-centre of the triangle formed by joining the points P (- 2, -3), Q (6, 1) and R (1, 6).