Solution:
a) Length of CD
The length of CD is the distance between point C and point D
The distance between two points is calculated by;
Substituting these values in the formula;
Therefore, the length of CD is 10 units
b) The equation of locus P
The locus of points equidistant from a fixed point is a Circle.
Hence, the locus of point P moving at an equal distance of 5 units from point D is a circle with centre D, and radius of 5 units.
The equation of a circle is given by;
Center D is (1,7)
Therefore, the equation of the locus P is;
c) Area of quadrilateral OABC.
The area of a polygon can be gotten if the vertices of the polygon are known.
The table below shows the points and the coordinates of the vertices of the polygon.
Applying the formula above by substituting these values into the equation,
Therefore, the area of the quadrilateral OABC is 70 square units