Question

points j and k are midpoints of the sides of triangle fgh. what is the value of y? 2 5 7 8

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side.
Here, \(JK\) is the mid - segment and \(GF\) is the third side. So, \(2(2y + 5)=5y+3\).

Step2: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(4y+10 = 5y+3\).

Step3: Solve for \(y\)

Subtract \(4y\) from both sides: \(4y - 4y+10=5y - 4y+3\), which gives \(10=y + 3\).
Then subtract 3 from both sides: \(y=10 - 3\).

Answer:

\(y = 7\), so the answer is \(7\).