Question

Point M is the midpoint of segment AC. Point M is located at (25.5, 60.1) and point C is located at (18.3, 72.5). What is the location of Point A ?

Answer 1

Answer:

$A = (32.7,47.7)$

Step-by-step explanation:

Given

$M = (25.5,60.1)$

$C = (18.3,72.5)$

Required

Determine the coordinates of A

Midpoint is calculated as thus:

$M(x,y) = (\frac{A_x + C_x}{2}, \frac{A_y + C_y}{2})$

Substitute the given values

$(25.5,60.1) = (\frac{A_x + 18.3}{2}, \frac{A_y + 72.5}{2})$

Multiply through by 2

$2 * (25.5,60.1) = (\frac{A_x + 18.3}{2}, \frac{A_y + 72.5}{2}) * 2$

$2 * (25.5,60.1) = (A_x + 18.3, A_y + 72.5)$

$(51,120.2) = (A_x + 18.3, A_y + 72.5)$

By comparison:

$A_x + 18.3 = 51$

$A_y + 72.5 = 120.2$

$A_x + 18.3 = 51$

$A_x = 51 - 18.3$

$A_x = 32.7$

$A_y + 72.5 = 120.2$

$A_y = 120.2 - 72.5$

$A_y = 47.7$

Hence:

$A = (32.7,47.7)$