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n200080 [17]
3 years ago
14

Find the values of y for which the distance between the point p2,-3 and q 10, y is 10 units

Mathematics
1 answer:
lina2011 [118]3 years ago
7 0

Answer:

y = - 9, y = 3

Step-by-step explanation:

Calculate distance d using the distance formula

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (10, y)

d = \sqrt{(10-2)^2+(y+3)^2}

   = \sqrt{8^2+(y+3)^2}

Given distance between points is 10, then

\sqrt{64 +(y+3)^2} = 10 ( square both sides )

64 + (y + 3)² = 100 ( subtract 64 from both sides )

(y + 3)² = 36 ( take the square root of both sides )

y + 3 = ± \sqrt{36} = ± 6 ( subtract 3 from both sides )

y = - 3 ± 6 , thus

y = - 3 - 6 = - 9

y = - 3 + 6 = 3

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