In triangle rst, u is the midpoint of rs, v is the midpoint of st, and w is the midpoint of tr. use the triangle diagram to answer the question. 1. what is the length of rs? a. 12 b. 6 c. 22 d. 24 2. what is the value of x? a. 6.5 b. 6 c. 11 d. 5.5 3. what is the value of y? a. 15.9 b. 11 c. 5.3 d. 3.7 4. what is the length of uw? a. 11 b. 6 c. 7.95 d. 22 5. what is the length of uv? a. 11 b. 6 c. 7.95 d. 12

(1)

we are given

U is the midpoint of RS

and we have

so, we can use formula

we can plug values

............Answer

(2)

V is the midpoint of ST

so, we get

now, we can plug values

divide both sides by 2

.........Answer

(3)

now, we can find y

W is the midpoint of TR

so, we get

we can plug value

divide both sides by 3

(4)

we can see that

triangles URW and RST are similar

so, their sides ratios must be equal

so, we get

we can plug values

...........Answer

(5)

we can see that

triangles SUV and RST are similar

so, their sides ratios must be equal

so, we get

now, we can plug values

.............Answer

1. The length of RS is 24 units.

2. The value of is 5.5.

3. The value of is 5.3.

4. The length of UW is 11.

5. The length of UV is 15.9.

According to the given figure-

1. U is the mid-point of RS so, the length of UR and US are equal.

Hence, the length of RS is 24 units.

2. V is the mid-point of ST so, the length of VS and VT are equal.

So,

Hence, the value of is 5.5.

3. W is the mid-point of RT so, the length of WR and WT are equal.

So,

Hence, the value of is 5.3.

4. As,

So, the length of the sides is proportional.

Hence, the length of UW is 11.

5.  As,

So, the length of the sides is proportional.

Hence, the length of UV is 15.9.

Learn more about similar triangles here:

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let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

i think the answer is b