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the figure is a kite. what is the length of the kite’s longer diagonal?

We are given a kite in the given figure.

We need to find the the length of the kite’s longer diagonal.

Note: The diagonals of a kite cuts at right angle.

Therefore, we need to find the perpendicular sides of those right triangles formed.

For above small right triangle, base is 12 and hypotenuse is 13.

Applying Pythagoras theorem:

12^2 +b^2 = 13^2

144 +b^2 = 169

b^2 = 169 - 144

b^2 = 25.

For big right triangle, base is 12 and hypotenuse is 37.

Applying Pythagoras theorem:

12^2 + b^2 = 37^2

144 + b^2 = 1369

b^2 = 1369 - 144

b^2 = 1225

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)