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The coordinates of the vertex W are (5 , -1)
Step-by-step explanation:
In the parallelogram, the diagonal bisect each other
To find a missing vertex in a parallelogram do that:
- Find the mid-point of a diagonal whose endpoints are given
- Use this mid-point to find the missing vertex
- The mid point rule is
∵ WXYZ is a parallelogram
∴ Its diagonals are WY and XZ
∵ The diagonal bisect each other
- That mean they have the same mid-point
∴ They intersect each other at their mid-point
∵ x = (-2 , -3) and z = (7 , 7)
∴ = -2 and
= 7
∴ = -3 and
= 7
- Substitute them in the rule of the mid point to find the
mid-point of XZ
∴
∴ The mid-point of diagonals WY and XZ is (2.5 , 2)
Let us use it to find the coordinates of vertex W
∵ W = (x , y) and Y = (0 , 5)
∴ = x and
= 0
∴ = y and
= 5
- Equate 2.5 by the rule of the x-coordinate of the mid-point
∵
- Multiply both sides by 2
∴ 5 = x + 0
∴ 5 = x
∴ The x-coordinate of point W is 5
- Equate 2 by the rule of the y-coordinate of the mid-point
∵
- Multiply both sides by 2
∴ 4 = y + 5
- Subtract 5 from both sides
∴ -1 = y
∴ The y-coordinate of point W is -1
The coordinates of the vertex W are (5 , -1)
Learn more:
You can learn more about the mid-point in brainly.com/question/10480770
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Answer:
We have the function,
On simplifying, we get,
i.e.
Thus, the standard form of the function is .
Now, the factors of the given functions are (x+1) and (x+5).
<em>Since, the intercept form of the function is the factored form of the function.</em>
So, we have, intercept form of the function is .
Now, we know that,
Value of x-coordinate of the vertex is i.e.
i.e.
i.e. x= -3
Then, i.e.
i.e. f(-3)=-4
So, the vertex of the function is (-3,-4).
Further, we know that,<em> 'the y-intercept of a function is the point where the function crosses y-axis'.</em>
So, when x=0, we have, i.e. f(0) = 5
Thus, the y-intercept is (0,5)
Also, <em>'the x-intercept of a function is the point where the function crossese x-axis'.</em>
Then, for f(x)=0, we have i.e.
i.e. x= -1 and x= -5
Thus, the x-intercept are (-1,0) and (-5,0).