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Alex
3 years ago
11

What is the length of the line segment with endpoints (7,-1) and (-3,5)?

Mathematics
1 answer:
Galina-37 [17]3 years ago
8 0

Formula to find the length of two endpoints: \sqrt{(x^2-x^1)^2+(y^2-y^1)^2}

Now, solve with the given endpoints.

\sqrt{(x^2-x^1)^2+(y^2-y^1)^2} \\\sqrt{(-3-7)^2+(5-(-1))^2} \\\sqrt{(-10)^2 + (6)^2} \\ \sqrt{100+36}\\\sqrt{136}

_______

Now, simplify using what we know about radicals.

Solution in picture.

_______

The length between the endpoints is 2√34 (Option B)

_______

Best Regards,

Wolfyy :)

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Answer:

Because BC=AD=8, segment BC ≅ Segment AD. Because these are horizontal line segments, their slopes are 0 and they are parallel.

Segment BC and AD are opposite sides that are both congruent and parallel. So ABCD is a parallelogram by the opposite sides congruent theorem.

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So if you count the boxes of segment BC you will get 8, same for if you count the boxes that make up segment AD. If they are the same distance they are congruent. You can see how BC and AD are both horizontal lines. To find the slope you need to do the slope formula for BC and AD, which is y2-y1/x2-x1 in our case BC= 4-4/12-4 which equals 0/8. If you do the same formula for AD, you will get 0/8 making them congruent and the slope 0. If the opposite sides are congruent and parallel it has to be a parallelogram by the opposites and congruent theorem.

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