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ValentinkaMS [17]
3 years ago
7

Given A(-2,3), B(m, 5) and C(-1,0). Find the possiblevalues of m if AB = 2AC.​

Mathematics
1 answer:
babymother [125]3 years ago
6 0

Answer:

m = 4 or m = -8

Step-by-step explanation:

length between 2 points = √(difference of x)² + (difference of y)²

AB² = (m - (-2))² + (5 - 3)² = (m + 2)² + 4 = m² + 4m +8

AC² = ((-1) - (-2))² + (0 - 3)² = 10

AB² = 4AC²

m² + 4m +8 = 40

m² + 4m - 32 = 0

(m - 4) (m + 8) = 0

m = 4 or m = -8

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(A) We let y = the cost and are told x = the number of people. Since you pay $20 per person, the cost is 20x. That is, y=20x

(B) Again, let the cost =y and the number of people is given as x. You pay $10 per person or 10x plus an additional $50 for the room. That is, y=10x+50

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(D) The admission price is the same when the two equations are equal. You can find this by setting them equal to each other as such: 20x = 10x+50 and solving for x. However, since you just graphed them the point of intersection (where the lines share/have the same point) gives the information. Remembers that (x,y) = (people, cost). The graphs intersect at (5, 100) so for 5 people the cost is the same and the cost is $100.

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