Question

Construct viable arguments. Given: A(2,5), B(0,0), and C(4,2).

Question a:

Find the coordinate of M, the midpoint of BC.

a) (2,2)
b) (2,1)
c) (2,3)
d) (2,4)

Answer 1

The coordinate of the midpoint M of line segment BC with endpoints B(0,0) and C(4,2) is calculated using the midpoint formula and results in M being (2, 1), which corresponds to option b.

Step-by-step explanation:

To find the coordinate of the midpoint M of the line segment BC with endpoints B(0,0) and C(4,2), we use the midpoint formula which states that the midpoint M(x, y) can be found using:

M(x, y) = \(\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

By substituting the given coordinates of B and C into the formula, we get:

M(x, y) = \(\left(\frac{0+4}{2}, \frac{0+2}{2}\right)\)

Then calculate the mean (average) of the x-coordinates and the y-coordinates of points B and C:

M(x, y) = \(\left(\frac{4}{2}, \frac{2}{2}\right)\) = (2, 1)

Therefore, the coordinate of the midpoint M of line segment BC is (2, 1), which matches option b.