Answer:
It is possible
Step-by-step explanation:
Every triangle has 180 degrees if you add the degrees of its angles, so it is possible with this data to construct a triangle
Answer:
the correct answer is (x,y) (3,-2)
The midpoint of a line divides the line into equal segments.
The option that proves PQ = LO is (a)
The given parameters are:
![\mathbf{L = (0,0)}](https://tex.z-dn.net/?f=%5Cmathbf%7BL%20%3D%20%280%2C0%29%7D)
![\mathbf{M = (3,0)}](https://tex.z-dn.net/?f=%5Cmathbf%7BM%20%3D%20%283%2C0%29%7D)
![\mathbf{N = (3,7)}](https://tex.z-dn.net/?f=%5Cmathbf%7BN%20%3D%20%283%2C7%29%7D)
![\mathbf{O = (0,7)}](https://tex.z-dn.net/?f=%5Cmathbf%7BO%20%3D%20%280%2C7%29%7D)
P is the midpoint of LM.
So, we have:
![\mathbf{P = \frac{LM}{2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%20%3D%20%5Cfrac%7BLM%7D%7B2%7D%7D)
![\mathbf{P = (\frac{(0 +3}{2},\frac{0+0}{2})}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%20%3D%20%28%5Cfrac%7B%280%20%2B3%7D%7B2%7D%2C%5Cfrac%7B0%2B0%7D%7B2%7D%29%7D)
![\mathbf{P = (\frac{3}{2},0)}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%20%3D%20%28%5Cfrac%7B3%7D%7B2%7D%2C0%29%7D)
Q is the midpoint of NO.
So, we have:
![\mathbf{Q = \frac{NO}{2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BQ%20%3D%20%5Cfrac%7BNO%7D%7B2%7D%7D)
![\mathbf{Q = (\frac{(3 +0}{2},\frac{7+7}{2})}](https://tex.z-dn.net/?f=%5Cmathbf%7BQ%20%3D%20%28%5Cfrac%7B%283%20%2B0%7D%7B2%7D%2C%5Cfrac%7B7%2B7%7D%7B2%7D%29%7D)
![\mathbf{Q = (\frac{3}{2},7)}](https://tex.z-dn.net/?f=%5Cmathbf%7BQ%20%3D%20%28%5Cfrac%7B3%7D%7B2%7D%2C7%29%7D)
Distance PQ is calculated as follows:
![\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bd%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D%7D)
This gives:
![\mathbf{PQ = \sqrt{(3/2 - 3/2)^2 + (0 - 7)^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%20%5Csqrt%7B%283%2F2%20-%203%2F2%29%5E2%20%2B%20%280%20-%207%29%5E2%7D%7D)
![\mathbf{PQ = \sqrt{ 7^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%20%5Csqrt%7B%207%5E2%7D%7D)
![\mathbf{PQ = 7}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%207%7D)
Distance LO is calculated as follows:
![\mathbf{LO = \sqrt{(0 - 0)^2 + (0 - 7)^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BLO%20%3D%20%5Csqrt%7B%280%20-%200%29%5E2%20%2B%20%280%20-%207%29%5E2%7D%7D)
![\mathbf{LO = \sqrt{ 7^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BLO%20%3D%20%5Csqrt%7B%207%5E2%7D%7D)
![\mathbf{LO=7}](https://tex.z-dn.net/?f=%5Cmathbf%7BLO%3D7%7D)
So, we have:
![\mathbf{PQ = 7}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%207%7D)
![\mathbf{LO=7}](https://tex.z-dn.net/?f=%5Cmathbf%7BLO%3D7%7D)
Thus:
![\mathbf{PQ = LO}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%20LO%7D)
Hence, the correct option is (a)
Read more about distance and midpoints at:
brainly.com/question/11231122
Answer:
The point-slope form of that line is y + 6 = -3/4(x - 2)
Step-by-step explanation:
When you have a point and the slope, you can find the point-slope form of the equation by simply putting the values in their correct spot using the base formula.
y - y1 = m(x - x1)
y - -6 = -3/4(x - 2)
y + 6 = -3/4(x - 2)