Q. 111 - Precalculus Enhanced with Graphing Utilities

Question

Drafting Error When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and subsequently will form an error triangle. If this

error triangle is long and thin, one estimate for the location of the desired point is the midpoint of the shortest side. The figure shows one such error triangle.

(a) Find an estimate for the desired intersection point.

(b) Find the length of the median for the midpoint found in part (a). See Problem 99.

Step-by-Step Solution

Answer

The intersecting point is $\left(2.65,1.6\right)$ and length of median is $1.285$

Step 1. Given Information

When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and subsequently will form an error triangle.

The figure shows one such error triangle.

Part (a) Step 1. Midpoint of the shortest side

$Midpoint=\left(\frac{2.7+2.6}{2},\frac{1.7+1.5}{2}\right)=\left(2.65,1.6\right)$

Part (b). Step 1. Finding length of median

$$\begin{gathered} length=\sqrt{{\left(2.65-1.4\right)}^2+{\left(1.6-1.3\right)}^2} \\ =\sqrt{1.4884+0.09}=\sqrt{1.5784}=1.285 \end{gathered}$$