If P is the midpoint of RS and RS=17x-8 and RP=8x+1, find the values of x and PS.
clearly
8x+1 = (1/2)(17x-8)
16x + 2 = 17x - 8
-x = -11
x = 11
PS = 17(11)-8 = 179
To find the values of x and PS, we need to apply the midpoint formula and use the given information.
Step 1: Apply the midpoint formula.
The midpoint formula states that the coordinates of the midpoint (P) of a line segment with endpoints (R) and (S) can be found by averaging the corresponding coordinates of R and S.
In this case, since we are given the lengths of RS and RP instead of their coordinates, we can use the formula for finding the midpoint based on the lengths of the line segments.
The formula is:
Midpoint = (R + S) / 2
Step 2: Substitute the given information into the midpoint formula.
We know that P is the midpoint of RS. Therefore, we can substitute the given lengths RS (17x - 8) and RP (8x + 1) into the formula:
(17x - 8 + 8x + 1) / 2 = RP
Simplify the equation:
(25x - 7) / 2 = RP
Step 3: Solve the equation for x.
To solve for x, we need to isolate it on one side of the equation. Multiply both sides of the equation by 2:
25x - 7 = 2 * RP
25x - 7 = 2(8x + 1)
25x - 7 = 16x + 2
Subtract 16x from both sides:
9x - 7 = 2
Add 7 to both sides:
9x = 9
Divide both sides by 9:
x = 1
Step 4: Calculate the value of PS.
Now that we have found the value of x, we can substitute it back into either RS or RP to find the length of PS.
Using RP = 8x + 1, substitute x = 1 into the equation:
RP = 8(1) + 1
RP = 8 + 1
RP = 9
Therefore, the value of PS is 9.