Question

find ir if is = 2x - 6 and ir = x - 2
triangle image with vertices r, s, q and point i on rs
value of x =
type your answer...
what is the length of segment sr?
type your answer...

Explanation:

Step1: Assume I is midpoint (from triangle)

Since \( I \) is the midpoint of \( SR \), \( IR = IS \)? Wait, no, wait—wait, the diagram: \( QI \) is a segment, so \( IR = IS \)? Wait, no, maybe \( IR = IS \)? Wait, the problem: Find \( IR \) if \( IS = 2x - 6 \) and \( IR = x - 2 \). Wait, maybe \( I \) is the midpoint, so \( IR = IS \)? Wait, no, maybe \( IR = IS \)? Wait, let's set \( IR = IS \)? Wait, no, maybe \( IR = IS \)? Wait, the problem says "Find \( IR \) if \( IS = 2x - 6 \) and \( IR = x - 2 \)". Wait, maybe \( I \) is the midpoint, so \( IR = IS \)? Wait, no, maybe \( IR = IS \)? Wait, let's solve \( 2x - 6 = x - 2 \)? Wait, no, that would be if \( IR = IS \), but maybe \( IR = IS \)? Wait, let's do the math.

Wait, maybe \( I \) is the midpoint of \( SR \), so \( IR = IS \). So set \( 2x - 6 = x - 2 \)? Wait, no, that would be \( 2x - 6 = x - 2 \), subtract \( x \): \( x - 6 = -2 \), add 6: \( x = 4 \). Then \( IR = x - 2 = 4 - 2 = 2 \). Wait, but then \( IS = 2(4) - 6 = 8 - 6 = 2 \), so \( IR = 2 \), \( IS = 2 \), so \( SR = IR + IS = 4 \). Wait, but the problem also asks for \( SR \). Wait, maybe \( I \) is the midpoint, so \( IR = IS \), so \( 2x - 6 = x - 2 \).

Step1: Set \( IS = IR \) (midpoint)

\( 2x - 6 = x - 2 \)

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( x - 6 = -2 \)
Add 6 to both sides: \( x = 4 \)

Step3: Find \( IR \)

\( IR = x - 2 = 4 - 2 = 2 \)

Step4: Find \( SR \)

Since \( I \) is midpoint, \( SR = IR + IS = 2 + 2 = 4 \)

Wait, but let's check. If \( x = 4 \), \( IS = 2(4) - 6 = 2 \), \( IR = 4 - 2 = 2 \), so \( SR = 2 + 2 = 4 \).

Answer:

For \( x \): 4
For \( SR \): 4

Wait, but the first part is "value of \( x = \)" and then "length of segment \( SR \)". So:

Value of \( x \): 4
Length of \( SR \): 4