Question

Please answer this question with how do work it out?

Answer 1

Answer:

Point B coordinates' are: (3.2, 1.6)

Step-by-step explanation:

Since this is a rhomboid the diagonals AC and OB, must be perpendicular to each other. Then we can find first the equation of the line where segment AC lies, seeing that this line will cross the y axis at the point (0,4), and the x axis at the point (2, 0). The line can then be obtained by calculating the slope of the segment that joins the two points, and then using that the line's y-intercept must be at the point (0, 4):

$slope=\frac{0-4}{2-0} =-2$

then the equation of the line for segment AC must be:

$y=-2x+4$

Next, we calculate the equation of a perpendicular line to the previous one, and that passes through the point (0, 0) to determine the equation of the line that contains the segment OB. Recall that the perpendicular line to one of slope m must have a slope given by: -1/m (the opposite of the reciprocal of "m". Then this new perpendicular line passing through (0, 0) must be given by:

$y=\frac{1}{2} x+0\\y=\frac{1}{2} x$

Now we can find the point at which both lines intersect:

$\frac{1}{2} x=-2x+4\\\frac{1}{2} x+2x=4\\\frac{5}{2} x = 4\\x=\frac{8}{5}$

and therefore the y value of the intersection point can be calculated via:

$y=\frac{1}{2} x\\y=\frac{1}{2} (\frac{8}{5} )\\y=\frac{4}{5}$

Then, point point B must be located at an x value that doubles the x value of the intersecting point, and similarly the y value of point B must be at the double of the value of the intersection point we just calculated. That is:

Point B = $(2\,*\frac{8}{5} ,\,2\,*\frac{4}{5} )=(\frac{16}{5} ,\frac{8}{5}) =(3.2,1.6)$

We can see the coordinates of point B and the lines we just generated in the attached image.