Question

1. practice: making mental images and summarizing diagonal segments the endpoints of a segment are (10, 3) and (20, 17). how do you know it is a diagonal segment? midpoint = (0,10). midpoint = (0,5).

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Identify the endpoints

The endpoints are $(x_1,y_1)=(10,3)$ and $(x_2,y_2)=(20,17)$.

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

$x=\frac{10 + 20}{2}=\frac{30}{2}=15$.

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

$y=\frac{3+17}{2}=\frac{20}{2}=10$.
So the mid - point of the segment with endpoints $(10,3)$ and $(20,17)$ is $(15,10)$. There is no clear way to determine if it is a diagonal segment just from the mid - point and endpoints given without additional context about the figure it belongs to. But if we assume we are working in a coordinate - based geometric figure, a diagonal segment is one that is not parallel to the x - axis or y - axis. The slope of the line passing through $(10,3)$ and $(20,17)$ is $m=\frac{17 - 3}{20 - 10}=\frac{14}{10}=\frac{7}{5}
eq0$ and $
eq\infty$, so it is not parallel to the x - axis or y - axis, suggesting it could be a diagonal segment of a polygon (like a rectangle, square etc.) in the coordinate plane.

Answer:

The mid - point of the segment with endpoints $(10,3)$ and $(20,17)$ is $(15,10)$. We can suspect it is a diagonal segment as its slope $\frac{7}{5}$ indicates it is not parallel to the x - axis or y - axis.