The points and are two vertices of a triangle

MATHEMATICS · Multi-part · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

The points

A(2,5)

and

B(8,1)

are two vertices of a triangle

ABC

. The median from the third vertex

C

to the side

AB

has slope

-\dfrac{3}{2}

and length

5

units. (i) Calculate the coordinates of the midpoint

M

AB

. (ii) Write the equation of the median

CM

in slope–intercept form. (iii) Using the fact that

CM=5

, determine the possible coordinates of

C

and hence describe the two admissible positions of the vertex

C

. Provide complete working.