Find the values of c and d

Question

Two points with the coordinates A (c, 2d + 2) and B (d , c - 3) have a midpoint with coordinates M(-2,4). 

Answer 1

A and C are the endpoints of a line with the midpoint.  A is point 1 and B is point 2.  To solve this, we use the midpoint formula.

 

 

M = ((x₁ + x₂) / 2  ,   (y₁ + y₂) / 2)

 

where M is the midpoint.

 

 

(-2, 4) = ((c + d) / 2  ,  ((2d + 2) + (c - 3)) / 2)

 

(-2, 4) = ((c + d) / 2  ,  (c + 2d - 1) / 2)

 

 

Next, set up equations according to x-coordinate and y-coordinate.

 

-2 = (c + d) / 2           and        4 = (c + 2d - 1) / 2

 

-4 = c + d                   and        8 = c + 2d - 1

                                               9 = c + 2d

 

 

We have 2 equations to work with now.

 

c + d = -4           eq1 

c + 2d = 9           eq2

 

 

Use elimination method.  Subtract eq2 from eq1 to eliminate the c terms.

 

-d = -13

 d = 13

 

 

Substitute this value of d into eq1 to solve for c.

 

c = -4 - d

c = -4 - 13

c = -17

 

 

These are our values of c and d.

 

c = -17

d = 13