8) The points and have coordinates (4, 6) and (12, 2) respectively. A B The straight line passes through and l1 A B a) Find an equation for in the form + = where and are integers l1 ax by c, a, b c [3] b) The straight line passes through the origin and has gradient l2 –4 Write down an equation for in the form l2 [1] c) The lines and intercept at the point l1 l2 C [4] Find the exact coordinates of the mid-point of AC Green 9) The diagram shows a rectangle The point lies on the y-axis and the points and lie on the x-axis Given that the straight line through the points and has equation a) Show that the straight line through points and has equation [4] b) Find the area of rectangle [3] 10) The points and have coordinates (2, and (8, 5) respectively, and is a A B AB –3) chord of a circle with centre as shown in Fig. 1. C, a) Find the gradient of [2] AB. Find the distance b) [2] AB The point is the mid-point of M AB c) Find an equation for the line through and in the form [5] C M d) Given that the of is 4, find the of [2] x-coordinate C y-coordinate C, e) Show that the radius of the circle is [4]
8) The points A and B have coordinates (4, 6) and (12, 2) respectively. The straight line l1 passes through A and B a) Find an equation for l1 in the form ax + by = c, where a, b and c are integers [3] b) The straight line l2 passes through the origin and has gradient –4 Write down an equation for l2 in the form [1] c) The lines l1 and l2 intercept at the point C Find the exact coordinates of the mid-point of AC [4] Green 9) The diagram shows a rectangle The point lies on the y-axis and the points and lie on the x-axis Given that the straight line through the points and has equation a) Show that the straight line through points and has equation [4] b) Find the area of rectangle [3] 10) The points A and B have coordinates (2, –3) and (8, 5) respectively, and AB is a chord of a circle with centre C, as shown in Fig. 1. a) Find the gradient of AB. [2] b) Find the distance AB [2] The point M is the mid-point of AB c) Find an equation for the line through C and M in the form [5] d) Given that the x-coordinate of C is 4, find the y-coordinate of C, [2] e) Show that the radius of the circle is [4]
a102_3-assessment-linear-geometry-qp.docx