Question

(a) Construct, using a compass and straightedge, the midpoint of UV and label it M. Then

Answer 1

Step-by-step explanation:

a) for the first part, you take your compass and stretch it more than halfway on to line UV. Place the fixed point at V and draw a curve. make sure you keep your compass the same size, put the fixed part of your compass on point U and draw a curve again. both curves should go both upward and downward. Now, your curves should meet at two points. use your straight edge to draw the line that meets at both points. I have drawn an example of what it should approximately look like. for the second part you are simply using your straight edge to draw a line from T down to the median M you previously found. I have drawn a second picture to show you.

b) now to check if they are perpendicular, we must find the slope of each line. I will not be able to do this accurately since I didn't use an exact method to find M, so you must follow my steps.

Step 1: find the slope of UV. To do so, we must take two points from the line. I will take points U and V because they are easiest to see. To find the slope, we can use the equation:

$m = \frac{y2 - y1}{x2 - x1}$

where m is the slope.

so, let's define our points.

Point V is (4,4), let's call this point one.

Point U is (14,6), let's call this point two.

So,

x1= 4

y1= 4

and

x2= 14

y2= 6

now, we can plug these into our slope equation.

$m = \frac{6 - 4}{14 - 4} = \frac{2}{10} = \frac{1}{5}$

You must then use the points T and M in order to solve the second slope. Where T is (2,12). I will keep M as (x1, y1) for now.

The equation should then look like:

$m = \frac{2 - y1}{12 - x1}$

now, in order for it to be perpendicular to our original slope, it must be the opposite reciprocal, which is the number flipped and made negative. The opposite reciprocal of 1/5 will be -5.

It should NOT be, as we have been told. So, we can state:

"I know that TM is not perpendicular to UV because the UV has a slope of 1/5 and TM has a slope of x, which is NOT the opposite reciprocal on 1/5."

Hope this helps! :)