Ac=ce and d is the midpoint of ce. if ce = 10x+18 de = 7x-1 and bc = 9x-3 find ab

The length of AB is 26units

The midpoint is a point that divides the line into two equal parts.

Given the following expressions

CE = 10x+18

DE = 7x-1

BC = 9x-3

if D is the midpoint of CE, then:

CD + DE = CE

Also CD = DE

DE + DE = CE

2DE = CE

2(7x-1) = 10x+18

14x-2 = 10x+18

14x-10x = 18+2

4x = 20

x = 20/4

x = 5

Also, we can make use of the expression:

AB + BC = AC

AB = AC - BC

Given the following:

BC = 9x - 3

CE = 10x + 18

Recall that AC=CE, hence AC = 10x + 18

AB = 10x+18-(9x-3)

AB = 10x + 18 - 9x + 3

AB = x + 18 + 3

AB = x + 21

Since x = 5

AB = 5 + 21

AB = 26

Hence the length of AB is 26

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We know the CE = 10x + 18 and DE = 7x - 1 and D is the midpoint of CE

⇒ CE = 2 * DE

⇒ 10x + 18 = 2 * (7x - 1)

⇒ 10x + 18 = 14x - 2

⇒ -4x = -20

⇒ x = 5

Now we also know that BC = 9x - 3 and AC = CE = 10x + 18

⇒ AB = AC - BC

⇒ AB = 10x + 18 - (9x - 3)

⇒ AB = x + 21

Substituting the value of x,

⇒ AB = 5 + 21

⇒ AB = 26

Hence, the value of AB is 26 units.

step-by-step explanation:

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