Question

leo is assembling a lamp, and after attaching the bottom and sides he must now insert the fixture that will hold the light - bulb. in order to ensure the light will shine evenly through the lamp, the fixture must be centered perfectly in the base. leo sets the lamp on the gridded table in his workshop and marks two points on the edge that are lined up to make a diameter of the circular bottom, as shown in the diagram below. if the two points leo marked were (21,33) and (35,17), where must he attach the fixture so that it will be centered?

Explanation:

Step1: Recall mid - point formula

The mid - point of a line segment with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ is given by $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Identify the endpoints

Here, $x_1=21,y_1 = 33,x_2=35,y_2 = 17$.

Step3: Calculate the x - coordinate of the mid - point

$x=\frac{21 + 35}{2}=\frac{56}{2}=28$.

Step4: Calculate the y - coordinate of the mid - point

$y=\frac{33+17}{2}=\frac{50}{2}=25$.

Answer:

$(28,25)$