Explanation
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
[tex]\text{ Slope }=\frac{\text{ rise}}{\text{ run}}[/tex]
Since the slope of the line segment AB is 3/4, we know that its rise is 3, and its run is 4.
[tex]\text{ Slope of line segment AB }=\frac{\text{ rise}}{\text{ run}}=\frac{3}{4}[/tex]
So, the coordinates of points A and B could be A(0,0) and B(4,3).
On the other hand, the rule for a rotation by 180° about the origin is:
[tex](x,y)\rightarrow(-x,-y)[/tex]
Then we can apply the above rule and calculate the coordinates of line segment A'B'.
[tex]\begin{gathered} A(0,0)\operatorname{\rightarrow}A^{\prime}(0,0) \\ B(4,3)\operatorname{\rightarrow}B^{\prime}(-4,-3) \end{gathered}[/tex]
Finally, let us find the slope of the line segment A'B'.
As we can see, the slope of the line segment A'B' is also 3/4.
[tex]\text{Slope of line segment A'B'}=\frac{\text{r\imaginaryI se}}{\text{run}}=\frac{3}{4}[/tex]Answer
Supports Jessie's claim
