What is the distance between 3x - 5y + 3 =0 and 6x - 10y -12 =0
1 answer:
9514 1404 393
Answer:
(9/34)√34 ≈ 1.543
Step-by-step explanation:
The second equation can be rewritten as ...
6x -10y -12 = 0
3x -5y -6 = 0
3x -5y = 6
__
The formula for the distance from point (x, y) to line ax+by+c=0 is ...
d = |ax+by+c|/√(a²+b²)
Then the distance from a point to the first line is ...
d = |3x -5y +3|/√(3² +(-5)²)
We know from the rearrangement of the second equation that points on its line satisfy (3x-5y) = 6. Substituting this value for (3x -5y) in the distance formula gives ...
d = |6 +3|/√34
Simplifying and rationalizing the denominator gives a distance of ...
d = (9/34)√34 ≈ 1.543
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Answer:
A = 35 square units
Step-by-step explanation:
Formula to calculate the distance between two points and
is,
d =
Length of the segment between A(2, 2) and B(9, 2) =
= 7 units
Length of the segment between B(9, 2) and C(9, -3) =
= 5 units
Length of the segment between C(9, -3) and D(2, -3) =
= 7 units
Length of the segment between A(2, 2) and D(2, -3) =
= 5 units
Therefore, given polygon is a rectangle.
Area of the rectangle = length × width
= 7 × 5
= 35 square units