Refer to the figure. If AB = 5 units, find the value of a.

Find the slope of the straight line passing through A and B in the figure.

Find the value of b in the figure.

Find $\theta$ in the figure, correct to 3 significant figures.

In the figure, the straight line L is parallel to AB. Find the slope of L.

In the figure, the straight line L is perpendicular to AB. Find the slope of L.

In the figure, M is the mid-point of AB. Find the coordinates of M.

In the figure, M is the mid-point of AB. Find the coordinates of A

In the figure, P is a point on the line segment AB such that AP : PB = 1 : 3. Find the coordinates of P.

In the figure, P is a point on the line segment AB such that AP : PB = 1 : 4. Find the coordinates of B.

Which of the following points can form an isosceles triangle?

I. A(-2, 4), B(8, -1), C(6, 10)

II. P(-3, 2), Q(6, 7), R(9, -5)

III. X(-11, 3), Y(-5, -3), Z(-2, 6)

The figure shows a circle with AB as its diameter. The coordinates of A and B are (-2, 4) and (6, -2) respectively. Find the area of the circle.

In the figure, L1 passes through the origin O and A(2, 4), while L2 passes through O and B(4, 2). Find  $\theta$  , correct to the nearest 0.1°.

Given four points A(3, -1), B(5, 2), C(-1, 6) and D(-3, 3), which of the following is/are correct?
    I.     AD // BC
    II.    AD $\perp$ CD
    III.  AC $\perp$ BD

In the figure, the origin O, A(2k, 4) and B(3, -2 - k) are the vertices of a triangle and  $\angle$ AOB = 90°. Find the length of AB.

M(6, 1) is the mid-point of the line segment joining A(2a - 1, 3a + 2) and B(3b + 2, -b). Then, a + b =

Consider two points A(-1, -5) and B(7, -1). AB is produced to meet the x-axis at C. Find AB : BC.

In the figure, A(1, 3), B(2, -3) and C(5, -1) are the vertices of a triangle. AC cuts the x-axis at P. Then, the area of △ABP : the area of △PBC =