Respuesta :
Answer:
The distance of vertical segments is found from the difference between the y-coordinate values, distance = y₂ - y₁
The distance for horizontal segments is found from the difference between the x-coordinate values, distance = x₂ - x₁
Step-by-step explanation:
The distance formula for finding the distance between two points with the given coordinates, (x₁, y₁), (x₂, y₂) can be presented as follows;
[tex]Distance =\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
For vertical segments, we have that the values of the x-coordinates are the same for both points, such as x₁ = x₂ which gives the distance between the points as follows;
[tex]Distance =\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}} \\\\ (x_1 = x_2) \\ \\\therefore Distance = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{2} \right )^{2}} =\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (0 \right )^{2}}\\\\Distance =\sqrt{\left (y_{2}-y_{1} \right )^{2}} = y_{2}-y_{1}[/tex]
Therefore, the distance of vertical segments is found by simply finding the difference between the y-coordinate values, distance = y₂ - y₁
Similarly, for horizontal segments, we have the values of the y-coordinates are the equal for both points, such as y₁ = y₂ which gives the distance between the points as follows;
[tex]Distance =\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}} \\\\ (y_1 = y_2) \\ \\\therefore Distance = \sqrt{\left (y_{2}-y_{2} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}} =\sqrt{\left (0 \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}\\\\Distance =\sqrt{\left (x_{2}-x_{1} \right )^{2}} = x_{2}-x_{1}[/tex]
The distance of horizontal segments is the difference between the x-coordinate values, distance = x₂ - x₁.
