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faust18 [17]
2 years ago
8

Find the value of x such that the area of a triangle whose vertices have coordinates (6, 5), (8, 2) and (x, 11) is 15 square uni

ts.
Mathematics
1 answer:
Serjik [45]2 years ago
3 0

Answer:

x =12\ or\ -8

Step-by-step explanation:

Given

(x_1,y_1) = (6,5)

(x_2,y_2) = (8,2)

(x_3,y_3) = (x,11)

Area = 15

Required

Find x

The area is calculated as thus:

Area = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|

Substitute values

15 = \frac{1}{2}|6*(2 - 11) + 8*(11 - 5) + x(5 - 2)|

15 = \frac{1}{2}|6*(-9) + 8*(6) + x(3)|

15 = \frac{1}{2}|-54 + 48 + 3x|

15 = \frac{1}{2}|-6 + 3x|

Multiply through by 2

2 * 15 = \frac{1}{2}|-6 + 3x| * 2

30 = |-6 + 3x|

Remove absolute sign

30 = -6 + 3x\ or\ -30 = -6 + 3x

Add 6 to both sides

36 = 3x\ or\ -24 =  3x

Divide by 3

12 = x\ or\ -8 = x

x =12\ or\ -8

<em>So, the coordinates are (-8, 11) or (12,11)</em>

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