If using the method of completing the square to solve the quadratic equation
1 answer:
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- The Midpoint of AB is (1,0).
Given that:
- In line AB, where the coordinates of A is (3,1) and coordinates of B is (-1,-1).
To find:
- The Midpoint of line AB.
So, according the question
We know that,
The midpoint M of a line segment AB with endpoints A (x₁, y₁) and B (x₂, y₂) has the coordinates M ( ).
Now from question,
We know that the the coordinates of A is (3,1) and coordinates of B is (-1,-1) of line AB.
So, we can say that
A is (3,1) or x₁ = 3 and y₁ = 1.
B (-1,-1) or x₂ = -1 and y₂ = -1.
∵ The coordinates of midpoint M (X,Y)
X =
=
= 2/2
X = 1.
And
Y =
=
= 0/2
Y = 0.
So, the midpoint of line AB is M (1,0)
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Answer:
- B) One solution
- The solution is (2, -2)
- The graph is below.
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Explanation:
I used GeoGebra to graph the two lines. Desmos is another free tool you can use. There are other graphing calculators out there to choose from as well.
Once you have the two lines graphed, notice that they cross at (2, -2) which is where the solution is located. This point is on both lines, so it satisfies both equations simultaneously. There's only one such intersection point, so there's only one solution.
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To graph these equations by hand, plug in various x values to find corresponding y values. For instance, if you plugged in x = 0 into the first equation, then,
y = (-3/2)x+1
y = (-3/2)*0+1
y = 1
The point (0,1) is on the first line. The point (2,-2) is also on this line. Draw a straight line through the two points to finish that equation. The other equation is handled in a similar fashion.
