in the diagram, the length of segment qv is 15 units. what is the length of segment tq? 4 units 11 units 14…

Explanation:

Step1: Set up equation for equal - length segments

Since the segments $ST$ and $SV$ are congruent (indicated by the tick - marks), we have $3x + 2=4x - 1$. $3x+2 = 4x - 1$ $2 + 1=4x-3x$ $x = 3$

Step2: Find length of $SR$

We know that point $R$ is the mid - point of $TV$ and $QR$ is perpendicular to $TV$. Triangles $STR$ and $SVR$ are congruent right - triangles. Also, triangles $TQR$ and $VQR$ are congruent right - triangles. We first find the length of $SV$ by substituting $x = 3$ into the expression for $SV$: $SV=4x - 1=4\times3-1=11$. In right - triangle $SVR$, we know $SV = 11$ and $QV = 15$. In right - triangle $TQR$ and $VQR$, since they are congruent, we can use the Pythagorean theorem in right - triangle $VQR$. But we can also use the property of congruent triangles. Since $\triangle TQR\cong\triangle VQR$, $TQ = VQ$.

Answer:

15 units