Question

If R is the midpoint of segment QS, QR = 6x - 20 and RS = 4x - 2, find Qs.

a) 10
b) 12
c) 14
d) 16

Answer 1

Upon calculating the values of x and determining the lengths of QR and RS, it is found that the length of QS is 68 units. However, this answer does not match any of the multiple choice options provided, suggesting a possible error in the options.

Step-by-step explanation:

If R is the midpoint of segment QS, then QR and RS are equal in length. Given that QR = 6x - 20 and RS = 4x - 2, we can set them equal to each other to solve for x:

6x - 20 = 4x - 2

Subtracting 4x from both sides gives us:

2x - 20 = -2

Adding 20 to both sides gives us:

2x = 18

Dividing both sides by 2 gives us:

x = 9

Now that we have the value for x, we can find the length of QR or RS by substituting 9 back into either equation. Let's use QR:

QR = 6(9) - 20

QR = 54 - 20

QR = 34

Since R is the midpoint, QS is twice the length of QR:

QS = 2(QR)

QS = 2(34)

QS = 68

Therefore, the length of QS is 68 units, which is not one of the options provided in the multiple choice answers. It seems there might be a typo or an error in the given options.