Please help will mark brainliest
2 answers:
Answer:
option 1) 1 7/8"
Step-by-step explanation:
its clearly visible that the green line covers 1 unit completely.
but it stops before it can reach 2 units.
check the attachment
- "mid point" is the mid point of 1 and 2 units
it will be at a distance of 1/ 2 units from the "unit 1".
( since 1 and 2 are 1 unit apart their mid point will lie exactly at rhe center that is 1/ 2 = 0.5)
- "second mid point" is the mid point of "mid point" and "unit 2".
since the "mid point" is at a distance of 0.5 units from "unit 2", second mid point will be at a distance of (1/ 2)/ 2 = 1/ 4 units from "mid point".
- now, third mid point is the mid point of "second mid point" and "unit 2"
since they're 1/ 4 units apart the third mid point will be (1/ 4)/2 units away from "second mid point"
and this is where the green line stops!
we got these points now well just add them up, to get the distance of required point from unit 1.
1/ 2 + 1/ 4 + 1/ 8
= 7/ 8
and this is in centimeters so add a " after it
1 7/ 8"
that is option 1.
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<h3>Given</h3>
- ΔABC
- A(-3, -1), B(0, 3), C(1, 2)
- the length of the perimeter of ΔABC to the nearest tenth
The perimeter of a triangle is the sum of the lengths of its sides. The length of each side can be found using the Pythagorean theorem. Effectively, each pair of points is treated as the end-points of the hypotenuse of a right triangle with legs parallel to the x- and y-axes. The leg lengths are the differences betweeen the x- and y- coordinates of the points.
The difference of the x-coordinates of segment AB are 0-(-3) = 3. The y-coordinate difference is 3-(-1) = 4. So, the leg lengths of the right triangle whose hypotenuse is segment AB are 3 and 4. The Pythagorean theorem tells us
... AB² = 3² +4² = 9 +16 = 25
... AB = √25 = 5
You may recognize this as the 3-4-5 triangle often introduced as one of the first ones you play with when you learn the Pythagorean theorem.
LIkewise, segment AC has coordinate differences of ...
... C - A = (1, 2) -(-3, -1) = (4, 3)
These are the same leg lengths (in the other order) as for segment AB, so its length is also 5.
Segment BC has coordinate differences ...
... C - B = (1, 2) -(0, 3) = (1, -1)
The length of the line segment is figured as the root of the sum of squares, even though one of the coordinate differences is negative. The leg lengths of the right triangle used for finding the length of BC are the absolute value of these differences, or 1 and 1. Then the length BC is
... BC = √(1² +1²) = √2 ≈ 1.4
So the perimeter of the triangle ABC is
... AB + BC + AC = 5 + 1.4 + 5 = 11.4 . . . . perimeter of ∆ABC in units
_____
Please be aware that the advice to "round each step" is <em>bad advice,</em> in general. For real-world math problems, you only round the final result. You always carry at least enough precision in the numbers to ensure that there will not be any error in the final rounding.
In this problem, the only number that is not an integer is √2, so it doesn't really matter.