Question

I desperately need this question answered. See attached image thanks so much

Answer 1

For this case we must follow the steps below:

step 1:

We place each of the given points on a coordinate axis

Step 2:

We join the AC points (represented by the orange line)

We join the BD points (represented by the blue line)

It is observed that the resulting figure after placing the 4 points on a coordinate axis, turns out to be a rhombus.

In addition, the blue and orange lines turn out to be perpendicular, that is, they have an angle of 90 degrees between them. This can be verified by finding the slopes of each of the two straight lines (blue and orange), which must be opposite reciprocal, that is, they comply: $m1 * m2 = -1$

In this case, the slope of the orange line is $m1 = 1$ and that of the blue line is $m2 = -1$

Then $m1 * m2 = 1 * -1 = -1$, it is verified that they are perpendicular.

Thus, the conclusion is that ABCD is a rhombus and AC is perpendicular to BD.

Answer:

See attached image

Option D