Question

W and Z are the midpoints of bar(OR) and bar(ST), respectively. Find the coordinates of W and Z.

Answer 1

Solution

Step 1:

Write the mid-point formula

$Coordinates\text{ of the mid-point = \lparen}\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\text{\rparen}$

Step 2:

W is a midpoint of OR

Coordinate of 0 = (0,0) and thw coordinate of R = (4a,4b)

$\begin{gathered} Coordinates\text{ of W = \lparen x, y\rparen} \\ \text{x = }\frac{4a\text{ + 0}}{2}\text{ = }\frac{4a}{2}\text{ = 2a} \\ y\text{ = }\frac{4b\text{ + 0}}{2}\text{ = }\frac{4b}{2}\text{ = 2b} \\ Coordinates\text{ of W = \lparen2a , 2b\rparen} \end{gathered}$

Step 3:

Z is the mid-point of TS

Coordinates of T = (4e, 0) and the coordinates of S = (4c, 4d)

$\begin{gathered} Coordinates\text{ of Z = \lparen x, y\rparen} \\ \text{x = }\frac{4c\text{ + 4e}}{2}\text{ = 2c + 2e} \\ y\text{ = }\frac{4d\text{ + 0}}{2}\text{ = }\frac{4d}{2}\text{ = 2d} \\ Coordinates\text{ of Z = \lparen2c+2e, 2d\rparen} \end{gathered}$

Final answer

c. W (2a , 2b) , Z (2c + 2e, 2d)