Question

given points a (1, 5) and b (-7, -5), which of the following coordinates is the midpoint of ab ?
(4, 0)
(-2, 0)
(-4, 0)
(2, 0)
(-3, 0)

Explanation:

Step1: Recall midpoint formula

The midpoint \( M(x_m, y_m) \) of two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( x_m=\frac{x_1 + x_2}{2} \), \( y_m=\frac{y_1 + y_2}{2} \).

Step2: Identify coordinates of A and B

For point \( A(1, 5) \), \( x_1 = 1 \), \( y_1 = 5 \); for point \( B(-7, -5) \), \( x_2=-7 \), \( y_2 = -5 \).

Step3: Calculate x - coordinate of midpoint

\( x_m=\frac{1+(-7)}{2}=\frac{1 - 7}{2}=\frac{-6}{2}=-3 \)? Wait, no, wait: \( 1+(-7)=1 - 7=-6 \), \( \frac{-6}{2}=-3 \)? Wait, no, wait the options have (-3,0)? Wait no, wait let's recalculate. Wait \( 1+(-7)= - 6 \), divided by 2 is -3? But the options have (-3,0) as one option? Wait no, wait the options are (4,0), (-2,0), (-4,0), (2,0), (-3,0). Wait, wait I must have miscalculated. Wait \( x_1 = 1 \), \( x_2=-7 \). \( x_m=\frac{1+(-7)}{2}=\frac{-6}{2}=-3 \). \( y_m=\frac{5+(-5)}{2}=\frac{0}{2}=0 \). So midpoint is (-3, 0). Wait but let's check again. \( 1 + (-7)= -6 \), divided by 2 is -3. \( 5 + (-5)=0 \), divided by 2 is 0. So midpoint is (-3, 0). Wait but in the options, the last option is (-3, 0). Wait maybe I misread the options. Let me check the options again: the options are (4,0), (-2,0), (-4,0), (2,0), (-3,0). Yes, so the midpoint is (-3, 0). Wait but wait, maybe I made a mistake. Wait \( x_1 = 1 \), \( x_2=-7 \). Sum is \( 1-7=-6 \), average is -3. \( y_1 = 5 \), \( y_2=-5 \), sum is 0, average is 0. So midpoint is (-3, 0).

Answer:

(-3, 0) (the last option, i.e., the option with coordinates (-3, 0))