If points f and g are symmetric with respect to the line y=x, then the line connecting f and g is perpendicular to y=x, and f and g are equidistant from y=x.
This problem could be solved graphically by graphing y=x and (8,-1). With a ruler, measure the perpendicular distance from y=x of (8,-1), and then plot point g that distance from y=x in the opposite direction. Read the coordinates of point g from the graph.
Alternatively, calculate the distance from y=x of (8,-1). As before, this distance is perpendicular to y=x and is measured along the line y= -x + b, where b is the vertical intercept of this line. What is b? y = -x + b must be satisfied by (8,-1): -1 = -8 + b, or b = 7. Then the line thru (8,-1) perpendicular to y=x is y = -x + 7. Where does this line intersect y = x?
y = x = y = -x + 7, or 2x = 7, or x = 3.5. Since y=x, the point of intersection of y=x and y= -x + 7 is (3.5, 3.5).
Use the distance formula to determine the distance between (3.5, 3.5) and (8, -1). This produces the answer to this question.
it’s 9 sq feet
use A=b•h/2
the base length is 6
the height is 3
6•3= 18 then divided by 2 is 9
4,000 × 2 = 8,000 hope thats what you meant!
Let's plug the given values and find value of y ~
or, you can further simplify it to ;
So the circle is really easy to graph. All you have to do is put a point at (1,2). Then another four points: 8 to the right of the center, 8 up from center, 8 left from center, and 8 down from center. Then contect the outer points.
The parabola is a little harder. So I can't see the equation very well, but I'm going to assume your vertix is correct. So put a point at (0,0).
The focus is 4 up from the center (0,4). The directrix is the same distance from the vertix as the focus, in the opposite direction. But it'll be horizontal or vertical line. This one I, believe, is y=-4.
So the parabola will open away from the directrix and towards the focus. You need two more points to graph this.
If I remember correctly, the other two points should be 2 x the focus/directrix distance. So 8, but even with the focus. Your other two points would be (0,12) (0, -4)
Then just connect the vertix to these two points. The only thing I need to double check is the distance betwen the focus with the two points.
