Question

find the error jacinda and elaine are finding the value of x in △ jhl. jacinda says that mp is one - half of jl so x is 4.5. elaine says that jl is one - half of mp so x is 18. is either of them correct? explain your reasoning.

Explanation:

Step1: Recall mid - segment theorem

In a triangle, a mid - segment (a line segment joining the mid - points of two sides of a triangle) is parallel to the third side and its length is half of the length of the third side. Here, if $MP$ is a mid - segment of $\triangle JHL$, then $MP=\frac{1}{2}JL$.

Step2: Identify the lengths

We know that $JL = 9$ and $MP=x$. According to the mid - segment theorem, $x=\frac{1}{2}\times9$.

Step3: Calculate the value of $x$

$x = 4.5$. Jacinda is correct because she correctly applied the mid - segment theorem which states that the mid - segment of a triangle is half the length of the third side. Elaine has the relationship between the mid - segment and the third side reversed.

Answer:

Jacinda is correct. The value of $x$ is $4.5$ because in a triangle, the mid - segment ($MP$) is half the length of the third side ($JL$), so $x=\frac{1}{2}\times9 = 4.5$.