Question

Point M is the midpoint of line PQ and has coordinates (1,a). Point P has coordinates (2a,-16). Point Q has coordinates (4b,2b). What is the value of a ?

Answer 1

To find the value of a, we use the fact that point M is the midpoint of line PQ. Simplifying the equation gives us a = 0.5.

Step-by-step explanation:

To find the value of a, we need to use the fact that point M is the midpoint of line PQ. The midpoint of a line segment is the average of the coordinates of the endpoints.

Given that point M has coordinates (1,a), and point P has coordinates (2a,-16), we can set up the following equation:

(1 + 2a)/2 = 2a

Simplifying this equation gives us:

1 + 2a = 4a3

Subtracting 2a from both sides gives:

1 = 2a

Dividing both sides by 2 gives:

a = 0.5