Answer: (x, y) transforms into (-x, y)
Step-by-step explanation:
When we do a reflection over a given axis, the distance between the initial point to the axis must be the same as the distance of the reflected point to the axis.
So if we do a reflection over the y-axis, then the value of y must be fixed.
So if we start with the point (x, y), the only other point that is at the same distance from the y-axis is the point (-x, y)
So the rule is, the y value remains equal and the x changes of sign.
If y = 6 when x = 8, then value of "x" when y = 9 is equal to 12
<u>Solution:</u>
Given that , In a certain function, y varies directly with x
And x = 8 when y = 6,
We have to find what will be the value of x when y = 9
Now, from the given information,
![\begin{array}{l}{y \alpha x} \\\\ {y=c x \rightarrow(1)}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7By%20%5Calpha%20x%7D%20%5C%5C%5C%5C%20%7By%3Dc%20x%20%5Crightarrow%281%29%7D%5Cend%7Barray%7D)
where c is the proportionality constant
![\begin{array}{l}{\text { Now, substitute } x=8 \text { and } y=6 \text { in }(1)} \\\\ {\rightarrow 8=c(6) \rightarrow c=\frac{8}{6}} \\\\ {\rightarrow c=\frac{4}{3}} \\\\ {\text { Then, }(1) \rightarrow x=\frac{4}{3} y} \\\\ {\text { So, when } y=9} \\\\ {\rightarrow x=\frac{4}{3}(9)} \\\\ {\rightarrow x=4 \times 3} \\\\ {\rightarrow x=12}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Ctext%20%7B%20Now%2C%20substitute%20%7D%20x%3D8%20%5Ctext%20%7B%20and%20%7D%20y%3D6%20%5Ctext%20%7B%20in%20%7D%281%29%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%208%3Dc%286%29%20%5Crightarrow%20c%3D%5Cfrac%7B8%7D%7B6%7D%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%20c%3D%5Cfrac%7B4%7D%7B3%7D%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20Then%2C%20%7D%281%29%20%5Crightarrow%20x%3D%5Cfrac%7B4%7D%7B3%7D%20y%7D%20%5C%5C%5C%5C%20%7B%5Ctext%20%7B%20So%2C%20when%20%7D%20y%3D9%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%20x%3D%5Cfrac%7B4%7D%7B3%7D%289%29%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%20x%3D4%20%5Ctimes%203%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%20x%3D12%7D%5Cend%7Barray%7D)
Hence, x value is 12 when y value is 9
This is a parabola which opens upwards and the directrix will be of the form
y = k
the general form is
4p(y - k) = (x - h)^2 we have:-
1/4(y + 3) = (x - 2)^2
so the vertex is at (2, -3)
4p = 1/4 so p = 1/16
so the focus will be at (2 , -2 15/16)
and directrix is y = -3 1/16
Answer:D
Step-by-step explanation:
students playing trombone=12+10+7+16
Students playing trombone=45