Chapter 8, Problem 2P

Solution

To find: whether the solution is full credit, partial credit, no credit.

The solution given is partial credit.

Given information:

The isosceles triangle $RST$ with $RT=ST$ the vertices are given as:

  $R\left(-2,2\right),S\left(4,-1\right),T\left(2,y\right)$

The given solution is below:

If $\Delta RST$ is an isosceles triangle with $RT=ST$ then $T$ lies on perpendicular bisector of $RS$ .

Midpoint of $RS=\left(\frac{-2+4}{2},\frac{-2+\left(-1\right)}{2}\right)$

Midpoint of $RS=\left(1,.05\right)$

Slope of $RS=\frac{-1-2}{4-\left(-2\right)}=-0.5$

Slope of Slope of $RS$

  $=\frac{-3}{6}$

Slope of Slope of $RS=-0.5$

The perpendicular bisector of $RS$ has a slope of 2,the negative reciprocal of -0.5.its equation is $y-0.5=2\left(x-1\right)$ .Substituting 2 for $x$ gives $y=2.5$ since $y=2x-1.5$ is a function, this is the only value of $y$ for $x=2$ .

Calculation:

The problem is solved for partial credit. There is the use of the formula of mid-point which is not explained. The concept of slope is not given and how the slope is found.

The equation of line is not explained only values have been put directly.