a) i) length of EF = 24.413
ii) coordinates of midpoint = (-3 , 5)
iii) coordinates of V(-13 , 12)
b) i) area if sides is given = 298
ii) area if diagonals is given = 298
From the below graph we will solve the problems
a) i)The formula to find the distance between the two points is given by
d = √[(x2 – x1)2 + (y2 – y1)2] (1)
where (x1 , y1) and (x2 , y2) are the coordinates
given that the coordinates are E(-10 , -5) and F(4 , 15)
putting the value in equation (1), we get
EF = √[(4 +10)2 + (15 + 5)2]
= √[(14)2 + (20)2]
= √(196 + 400)
= √596
EF = 24.413
ii) The formula for the midpoint is given by
(xm , ym) = [(x1 + x2)/2 , (y1 + y2)/2] (2)
Where (xm , ym) are the coordinates of the mid point.
given that the coordinates are E(-10 , -5) and F(4 , 15)
putting the value in equation (2), we get
(xm , ym) = {[(-10) + 4]/2 , [(-5) + 15]}
(xm , ym) = ( -6/2 , 10/2)
(xm , ym) = (-3 , 5)
iii) We have been given the coordinate of W(7 , -2) which is (x1 , y1)
and the coordinate of the midpoint which is (-3 , 5) which is (xm , ym)
to find the coordinate of V we will put the values in equation (2), we get
(-3 , 5) = [(7 + x2)/2 , (-2 + y2)/2]
Which is , -3 = (7 +x2)/2 5 = (-2 + y2)/2
-3 * 2 = 7 + x2 5*2 = -2 + y2
-6 – 7 = x2 10 + 2 = y2
-13 = x2 12 = y2
Therefore the coordinates of V(-13 , 12)
b) i) As the sides of a square are all same , area of square is the side length squared.
Applying the formula as equation (1), we get the length of EV
EV = √[(-13 +10)2 + (12 + 5)2]
= √[(-3)2 + (17)2]
= √(9 + 289)
= √298
= 17.26
Hence the area of the square is = (side)2
=(17.26)2
= 298
ii) The formula of area of square is given by = d2/2 (3)
where d = length of the diagonal of square.
As EF is the diagonal of the square, therefore,
d = EF = 24.143
Putting this value in equation (3), we get
Area = (24.143)2/2
= 596/2
Area = 298
learn more about area of square here : https://brainly.com/question/25092270
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