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Oliga [24]
3 years ago
12

Find the coordinates for the midpoint of the segment with endpoints give (3,5) and (-2,0)

Mathematics
1 answer:
Leto [7]3 years ago
8 0

Answer:

The coordinates of the mid-point are :

(\frac{1}{2}, \frac{5}{2})

Step-by-step explanation:

We know that, the coordinates of the mid-point (<em>x</em>, <em>y</em>) of a line segment joining the points (<em>x</em>₁, <em>y</em>₁) and (<em>x</em>₂, <em>y</em>₂) is given by

(x, y) = (\frac{x_{1} +x_{2} }{2},\frac{y_{1}+y_{2} }{2} )

Now, we have the given points as (3, 5) and (-2, 0).

By using the above formula, coordinates of the mid-point (<em>x</em>, <em>y</em>) of the line-segment joining the points (3, 5) and (-2, 0) is given by,

x = \frac{3+(-2)}{2} = \frac{3-2}{2} = \frac{1}{2}

y = \frac{5+0}{2} = \frac{5}{2}

∴ coordinates of the mid-point of the line-segment joining the points (3,5) and (-2,0) is (\frac{1}{2}, \frac{5}{2}).

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Is the following function even, odd or neither? f(x)=x^3 +4x
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D, neither

Step-by-step explanation:

to determine whether a function is even, odd or neither, we need to know what it means

an even function is symmetric with respect to the y-axis

an odd function is symmetric with respect to the origin

to solve an equation to see if its even or odd, we would need to substitute <em>x</em> in the equation for <em>-x</em>.

in an even function when we substitute f(-x), it should be equal to to f(x)

in an odd function when we substitute f(-x), it should be equal to -f(x)

so lets test the function given to see if its even

f(x) = x³ + 4x

f(-x) = (-x)³ + 4(-x)

f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to the orignal function, we see that f(-x) = x³ - 4x is not even as we did not get the same output as the original function

now we should test to see if its odd. we have already seen what f(-x) is, now lets try -f(x) and compare it to f(-x) and f(x)

-f(x) = -(x³ + 4x) -->

-f(x) = -x³ - 4x ≠ f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to f(x) and f(-x), we see that it not odd as we did not get the same output

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3 years ago
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