Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other? The length of SP, PQ, RQ, an
2 answers:
Answer:
Step-by-step explanation:
Given is a square PQRS. Its diagonals are PR and QS.
To prove that PR is perpendicular to QS
We have been given as
SP = PQ =RQ =SR =5.
Using Pythagorean theorem we have
both diagonals will equal
If P is the origin, (say) then coordinates of vertices would be (0,0) (5,0) (5,5) and (0,5)
Mid point would be (2.5,2.5) for both
Slope of RP = change in y coordinate/change in x coordinate
= 1
Slope of QS = 5/-5 = -1
Product of the two slopes = -1
Hence the two diagonals are perpendicular
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So the right options are:
Further explanation:
Given equation of line is:
2x+5y=10
We have to convert it into point-slope form
The co-efficient of x is the slope of the line
So,
As the required line is parallel to given line, it will also have same slope.
Let m1 be the slope of required line
Then the line will be:
Putting the value of slope
Putting (-5,1) in the equation to find the value of b
Putting the values of slope and b in equation
Multiplying the whole equation by 5 will give us:
5y = -2x-5
2x+5y = -5
Another form of equation of line is Point-slope form
Putting the values of slope and point in the equation, we get
So the right options are:
Keywords: Point-Slope form, Parallel lines
Learn more about point slope form at:
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