As given by the question
There are given that the point of two-line
![\begin{gathered} (1,\text{ 7) and (5, 5)} \\ (-1,\text{ -3) and (1, 1)} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%281%2C%5Ctext%7B%207%29%20and%20%285%2C%205%29%7D%20%5C%5C%20%28-1%2C%5Ctext%7B%20-3%29%20and%20%281%2C%201%29%7D%20%5Cend%7Bgathered%7D)
Now,
From the condition of a parallel and perpendicular line
If the slopes are equal then the lines are parallel
If the slopes are negative reciprocal then the lines are perpendicular
If the slopes are neither of the above are true then lines are neither
Then,
First, find the slope of both of line
So,
For first-line, from the formula of slope
![\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ m_1=\frac{5_{}-7_{}}{5_{}-1_{}} \\ m_1=-\frac{2}{4} \\ m_1=-\frac{1}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20m_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%5C%5C%20m_1%3D%5Cfrac%7B5_%7B%7D-7_%7B%7D%7D%7B5_%7B%7D-1_%7B%7D%7D%20%5C%5C%20m_1%3D-%5Cfrac%7B2%7D%7B4%7D%20%5C%5C%20m_1%3D-%5Cfrac%7B1%7D%7B2%7D%20%5Cend%7Bgathered%7D)
Now,
For second-line,
![\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ m_1=\frac{1_{}-(-3)_{}}{1-(-1)_{}} \\ m_1=\frac{4}{2} \\ m_1=2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20m_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%5C%5C%20m_1%3D%5Cfrac%7B1_%7B%7D-%28-3%29_%7B%7D%7D%7B1-%28-1%29_%7B%7D%7D%20%5C%5C%20m_1%3D%5Cfrac%7B4%7D%7B2%7D%20%5C%5C%20m_1%3D2%20%5Cend%7Bgathered%7D)
The given result of the slope is negative reciprocal because
![\begin{gathered} -\frac{1}{2}=-(-\frac{2}{1}) \\ -\frac{1}{2}=2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20-%5Cfrac%7B1%7D%7B2%7D%3D-%28-%5Cfrac%7B2%7D%7B1%7D%29%20%5C%5C%20-%5Cfrac%7B1%7D%7B2%7D%3D2%20%5Cend%7Bgathered%7D)
Hence, the slope of line1 is -1/2, and slope of line2 is 2 and the lines are perpendicular.
Answer:
The constant of variation is 5
Step-by-step explanation:
We know direct variation is of the form
y = kx
We know y =25 and x=5
25 = k*5
Divide each side by 5
25/5 = 5k/5
5 = k
Answer:
18.
Step-by-step explanation:
1) formula of the perimeter given in the condition is:
p=2(VW+XV) or p=2(VY+XY).
Note, VW=XY and XV=VY;
2) if to substitute p=84, VW=2z+2 and XV=3z into the formula above, then
2(2z+2+3z)=84, ⇔ 5z+2=42; ⇒ z=8.
3) if z=8, then VW=2z+2=2*8+2=18.