Question

The coordinates of the vertices of triangle ABC are A (1,-1),B (1,4), and C (8,4). what is the length in units of the line segment that connects vertex A and vertex B

Answer 1

The length of the line segment that connects vertex A and vertex B is 5 units

Step-by-step explanation:

Let us revise some facts about the horizontal and vertical segments

• The segment is horizontal if the y-coordinates of all points on the segment are equal
• The length of the horizontal segment whose endpoints are $(x_{1},y)$ and $(x_{2},y)$ is $x_{2}-x_{1}$
• The segment is vertical if the x-coordinates of all points on the segment are equal
• The length of the vertical segment whose endpoints are $(x,y_{1})$ and $(x,y_{2})$ is $y_{2}-y_{1}$

In Δ ABC

∵ A = (1 , -1)

∵ B = (1 , 4)

∵ C = (8 , 4)

∵ The x-coordinate of point A = 1

∵ The x-coordinate of point B = 1

∴ The x-coordinates of points A and B are equal

- The x-coordinates of A and B are equal, then the line AB is a

  vertical segment

∴ The length of AB is the difference between the y-coordinates

   of points A and B

∵ The y-coordinate of point A = -1

∵ The y-coordinate ob point B = 4

∴ The length of AB = 4 - (-1)

∴ The length of AB = 4 + 1

∴ The length of AB = 5 units

The length of the line segment that connects vertex A and vertex B is 5 units

Learn more:

You can learn more about the length of the segments in brainly.com/question/6564657

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