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.
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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