Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.