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Please solve with explanation will give brainliest

Please Solve With Explanation Will Give Brainliest class=

Sagot :

LammettHash

D is the midpoint of A and B, so it has coordinates

D ((0 +0)/2, (9 + 0)/2) = D (0, 9/2)

and E is the midpoint of B and C, so its coordinates are

E ((0 + 13)/2, (0 + 0)/2) = E (13/2, 0)

(a) The slope of the line through C and D is

(9/2 - 0)/(0 - 13) = -9/26

Then the equation of the line through C and D is

y - 0 = -9/26 (x - 13)

y = -9/26 x + 9/2

(b) I assume this part is asking about the coordinates of F as the intersection of AE and CD.

First find the equation of the line through A and E. It has slope

(9 - 0)/(0 - 13/2) = -18/13

so its equation is

y - 0 = -18/13 (x - 13/2)

y = -18/13 x + 9

Solve for the x-coordinate of F:

-9/26 x + 9/2 = -18/13 x + 9

(-9/26 + 18/13) x = 9 - 9/2

(36 - 9)/26 x = 9/2

27/26 x = 9/2

x = (9/2)/(27/26)

x = 13/3

Then use either line equation to solve for the y-coordinate:

y = -9/26 (13/3) + 9/2

y = -39/26 + 9/2

y = (117 - 39)/26

y = 78/26

y = 3

So F is the point (13/3, 3).

(c) Triangle ABC has height 9 and length 13, so its area is

1/2 • 9 • 13 = 117/2

(d) Triangle BCD has area

1/2 • 9/2 • 13 = 117/4

Triangle ECF has height 3 (the y-coordinate of F) and length 13 - 13/2 = 13/2 (the difference between the x-coordinate of C and E), so its area is

1/2 • 3 • 13/2 = 39/4

The area of BCD is the sum of the areas of quadrilateral DBEF and triangle ECF. So the area of DBEF is

117/4 - 39/4 = (117 - 39)/4 = 78/4 = 39/2

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