Answer:
The area of the triangle is of 21 units of area.
Step-by-step explanation:
The area of a triangle with three vertices
is given by the determinant of the following matrix:
![A = \pm 0.5 \left|\begin{array}{ccc}x_1&y_1&1\\x_2&y_2&1\\1_3&y_3&1\end{array}\right|](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7Dx_1%26y_1%261%5C%5Cx_2%26y_2%261%5C%5C1_3%26y_3%261%5Cend%7Barray%7D%5Cright%7C)
In this question:
Vertices (3,0) (9,0) (7,6). So
![A = \pm 0.5 \left|\begin{array}{ccc}3&0&1\\9&0&1\\7&7&1\end{array}\right|](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D3%260%261%5C%5C9%260%261%5C%5C7%267%261%5Cend%7Barray%7D%5Cright%7C)
![A = \pm 0.5(3*0*1+0*1*7+1*9*7-0*7*1-0*9*1-3*1*7)](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%283%2A0%2A1%2B0%2A1%2A7%2B1%2A9%2A7-0%2A7%2A1-0%2A9%2A1-3%2A1%2A7%29)
![A = \pm 0.5*(63-21)](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%2A%2863-21%29)
![A = \pm 0.5*42 = 21](https://tex.z-dn.net/?f=A%20%3D%20%5Cpm%200.5%2A42%20%3D%2021)
The area of the triangle is of 21 units of area.
Equation of the line that includes points (1, 1) and (1, 5) is a vertical line given by x = 1.
X+6+2x+4+x+3= 180
4x+13=180
4x= 167
x=41.75
Angle ABC= 47.75
Angle CBD= 87.5
Answer:
the slope of the two points is ![-\frac{7}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B7%7D%7B2%7D)
Step-by-step explanation:
to find the slope of two points you have to subtract them (x1,y1), (x2,y2)
Steps:
![(X_1,Y_1) (X_2, Y_2)](https://tex.z-dn.net/?f=%28X_1%2CY_1%29%20%28X_2%2C%20Y_2%29)
![\frac{3 - 10}{8 - 7} = -\frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%20-%2010%7D%7B8%20-%207%7D%20%3D%20-%5Cfrac%7B7%7D%7B2%7D)