1.) what is the length of the line segment whose endpoints are (1,1) and (3,-3)?

2.) what are the coordinates of the midpoint of the line segment whose endpoints are (c,0) and (0,d)?

3.) The diagonals of a rhombus have lengths of 8 cm and 6 cm. The perimeter of the rhombus is?

4.) ABCD is a rectangle, E is a point on CD, the measure of angle DAE = 30 degrees and measure of angle CBE= 20 degrees. What is the measure of angle x?

Tutors don't mind helping with some individual questions, but we are not prepared to do an assignment for you nor to do your homework for you.

I gave you the formulas for #1 and #2 when you posted under the name of Taylor
http://www.jiskha.com/display.cgi?id=1329662216

What part of just plugging in the above numbers do you have difficulties with ?

for #3, the diagonals of a rhombus bisect each other at right angles. Make a sketch to see 4 right-angled triangles, then use Pythagoras to find the length of the sides of the rhombus.

In #4, I have no clue where x is.
However, all angles can be found quite easily.

1.) To find the length of a line segment with given endpoints, you can use the distance formula. The distance formula is derived from the Pythagorean theorem. The formula for calculating the distance (d) between two points (x1, y1) and (x2, y2) in a 2-dimensional space is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the endpoints are (1, 1) and (3, -3). Plugging the coordinates into the distance formula, we have:

d = √((3 - 1)^2 + (-3 - 1)^2)
= √(2^2 + (-4)^2)
= √(4 + 16)
= √20
≈ 4.47

Therefore, the length of the line segment is approximately 4.47 units.

2.) The midpoint of a line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints. In this case, the endpoints are (c, 0) and (0, d). The midpoint coordinates would be:

x-coordinate: (c + 0)/2 = c/2
y-coordinate: (0 + d)/2 = d/2

Therefore, the coordinates of the midpoint are (c/2, d/2).

3.) In a rhombus, the diagonals are perpendicular bisectors of each other. Therefore, the diagonals divide the rhombus into four congruent right-angled triangles. Using the Pythagorean theorem, you can find the lengths of the sides of these triangles.

Let one of the sides of the rhombus be 'a'. Then, the length of one diagonal is equal to 2a, and the length of the other diagonal is equal to 2b, where 'b' is another side of the rhombus. The perimeter of the rhombus is given by 4a.

In this case, given the lengths of the diagonals as 8 cm and 6 cm, we can let 2a = 8 and 2b = 6. Solving for 'a' and 'b':

2a = 8
a = 4

2b = 6
b = 3

Therefore, the perimeter of the rhombus is 4a = 4 * 4 = 16 cm.

4.) In a rectangle, opposite angles are equal. Since angle DAE is 30 degrees and angle CBE is 20 degrees, angle AED can be calculated as:

angle AED = 180 - (angle DAE + angle CBE)
= 180 - (30 + 20)
= 130 degrees

Since ABCD is a rectangle, angle AED is equal to angle AEB. Therefore, angle x is also equal to 130 degrees.