Given:
M=(x1, y1)=(-2,-1),
N=(x2, y2)=(3,1),
M'=(x3, y3)= (0,2),
N'=(x4, y4)=(5, 4).
We can prove MN and M'N' have the same length by proving that the points form the vertices of a parallelogram.
For a parallelogram, opposite sides are equal
If we prove that the quadrilateral MNN'M' forms a parallellogram, then MN and M'N' will be the oppposite sides. So, we can prove that MN=M'N'.
To prove MNN'M' is a parallelogram, we have to first prove that two pairs of opposite sides are parallel,
Slope of MN= Slope of M'N'.
Slope of MM'=NN'.

Hence, slope of MN=Slope of M'N' and therefore, MN parallel to M'N'

Hence, slope of MM'=Slope of NN' nd therefore, MM' parallel to NN'.
Since both pairs of opposite sides of MNN'M' are parallel, MM'N'N is a parallelogram.
Since the opposite sides are of equal length in a parallelogram, it is proved that segments MN and M'N' have the same length.
Step-by-step explanation:
1. y--7=-2(x-0)
y+7=-2x
y=-2x-7
2. y--3=-2(x-1)
y+3=-2x+2
y=-2x+2-3
y=-2x-1
Given: a quadratic function with vertex (2,3) opening upward .
Find: the given statement is true or false.
Explanation: if parabola has a vertex at (2,3) and opens upward, it has one real solution., (2,3) will be a lowest point. The vertex will be at lowest point, it will be minimum.
that means graph has no one real solution. hence it will never going to intersect. so this statement is false.
Final answer: the given statement is FALSE.
Answer:
The correct option is b.
Step-by-step explanation:
The given function is

We need to find the value of f(-2). It means we have to find the value of given function at x=-2.
Substitute x=-2 in the given function to find the value of f(-2).

On simplification we get


The value of f(-2) is 11. Therefore the correct option is b.