Question

identify triangle from coordinates
( level 1 )
find the desired slopes and lengths, then fill in the words that characterize the triangle.
slope of \\( \overline { p q } = \\)
length of \\( \overline { p q } = \\)
slope of \\( \overline { q r } = \\)
length of \\( \overline { q r } = \\)
slope of \\( \overline { r p } = \\)
length of \\( \overline { r p } = \\)
answer attempt 1 out of 2
triangle \\( p q r \\) is

Explanation:

Step1: Calculate the slope of \( \overline{PQ} \)

The formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \( P(0,3) \) and \( Q(5,1) \). Then \( m_{PQ}=\frac{1 - 3}{5 - 0}=\frac{-2}{5}\) (There is an error in the given slope of \( \overline{PQ}\) in the original answer attempt).

Step2: Calculate the length of \( \overline{PQ} \)

The distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). For \( P(0,3) \) and \( Q(5,1) \), \( d_{PQ}=\sqrt{(5 - 0)^2+(1 - 3)^2}=\sqrt{25 + 4}=\sqrt{29}\) (There is an error in the given length of \( \overline{PQ}\) in the original answer attempt).

Step3: Calculate the slope of \( \overline{QR} \)

Let \( Q(5,1) \) and \( R(1,2) \). Then \( m_{QR}=\frac{2 - 1}{1 - 5}=\frac{1}{-4}=-\frac{1}{4}\) (There is an error in the given slope of \( \overline{QR}\) in the original answer attempt).

Step4: Calculate the length of \( \overline{QR} \)

For \( Q(5,1) \) and \( R(1,2) \), \( d_{QR}=\sqrt{(1 - 5)^2+(2 - 1)^2}=\sqrt{16 + 1}=\sqrt{17}\) (There is an error in the given length of \( \overline{QR}\) in the original answer attempt).

Step5: Calculate the slope of \( \overline{RP} \)

Let \( R(1,2) \) and \( P(0,3) \). Then \( m_{RP}=\frac{3 - 2}{0 - 1}=- 1\).

Step6: Calculate the length of \( \overline{RP} \)

For \( R(1,2) \) and \( P(0,3) \), \( d_{RP}=\sqrt{(0 - 1)^2+(3 - 2)^2}=\sqrt{1+1}=\sqrt{2}\) (There is an error in the given length of \( \overline{RP}\) in the original answer attempt).

Answer:

slope of \( \overline{PQ}=-\frac{2}{5}\), length of \( \overline{PQ}=\sqrt{29}\), slope of \( \overline{QR}=-\frac{1}{4}\), length of \( \overline{QR}=\sqrt{17}\), slope of \( \overline{RP}=-1\), length of \( \overline{RP}=\sqrt{2}\)