Question

five points are shown on a number - line. information about some of the lengths of different segments is given. the length of pq is 5 units. the length of rs is equal to the length of pq. the length of st is 3 times the length of qr. the length of pt is 25 units. which statements are correct? select all that apply. a. the length of qr is 3 units. b. the length of rs is 5 units. c. the length of qs is 19 units. d. the length of rt is 13 units. e. the length of st is 9 units.

Explanation:

Step1: Let the length of $QR = x$.

Let $QR=x$.

Step2: Express other segment - lengths in terms of $x$.

$PQ = 5$, $RS=QR=x$, $ST = 3x$, and $PT=25$.

Step3: Use the fact that $PT=PQ + QR+RS + ST$.

$25=5 + x+x + 3x$.

Step4: Simplify the equation.

$25=5 + 5x$.

Step5: Solve for $x$.

Subtract 5 from both sides: $25 - 5=5x$, so $20 = 5x$. Then $x = 4$.

Step6: Calculate the lengths of each segment.

$QR=x = 4$; $RS=x = 4$; $QS=QR + RS=4 + 4=8$; $RT=RS + ST=4+3\times4=4 + 12 = 16$; $ST = 3x=12$.

Answer:

None of the given statements (A - E) are correct.