Find the value of yif S is the midpoint of RT, T is the midpoint of RU,RS = 6x-7, ST = 3x+ 14 and TU = 4y+6.
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Since S bisects RT, RS=ST, so
6x-7 = 3x+14
x = 7
So, RS=35, and RT=70
Since T bisects RU, 4y+6 = 70, so y = 16
To find the value of y, we can use the fact that S is the midpoint of RT and T is the midpoint of RU.
Let's break down the information given:
- RS = 6x - 7
- ST = 3x + 14
- TU = 4y + 6
Since S is the midpoint of RT, we know that RS = ST. Therefore, we can set up an equation:
6x - 7 = 3x + 14
Now let's solve for x:
6x - 3x = 14 + 7
3x = 21
x = 7
Now that we have the value of x, we can substitute it back into one of the equations to find the value of y.
Let's use the equation TU = 4y + 6:
TU = 4y + 6
Substituting x = 7:
4(7) + 6 = 4y + 6
28 + 6 = 4y + 6
34 = 4y
Now we can solve for y:
4y = 34
y = 34/4
y = 8.5
Therefore, the value of y is 8.5.