Question

If the coordinates of the mid-points of the sides of the triangle be (3,-2), (-3,1) and (4,-3), then the coordinates of its vertices are?

Answer 1

the coordinates of the midpoint of the sides of the triangle be (3, -2) , (-3, 1) and (4, -3).

To find : the coordinates of its vertices are ....

solution : let (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the vertices of triangle.

using midpoint section formula,

(x, y) = [(x₁ + x₂)/2, (y₁ + y₂)/2 ]

let (3, -2) is the midpoint of (x₁, y₁) and (x₂, y₂).

so, (3, -2) = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(x₁ + x₂)/2 = 3 ⇒(x₁ + x₂) = 6 ......(1)

(y₁ + y₂)/2 = -2 ⇒ (y₁ + y₂) = -4 .....(2)

similarly, (-3, 1) is the midpoint of (x₂, y₂) and (x₃, y₃).

so (x₂ + x₃) = -6 .....(3)

(y₂ + y₃) = 2 ...........(4)

and (4, -3) is the midpoint of (x₃, y₃) and (x₁, y₁).

so, (x₁ + x₃) = 8 .......(5)

(y₁ + y₃) = -6 ........(6)

adding equations (1), (3) and (5) we get,

x₁ + x₂ + x₃ = (6 - 6 + 8)/2 = 4 ........(7)

subtracting eq (1) from (7) we get,

x₃ = 4 - 6 = -2

subtracting eq (3) from (7) we get,

x₁ = 4 + 6 = 10

subtracting eq (5) from (7) we get,

x₂ = 4 - 8 = -4

similarly adding equations (2), (4) and (6) we get,

y₁ + y₂ + y₃ = (-4 + 2 - 6)/2 = -4 .........(8)

subtracting eq (2) from (8) we get,

y₃ = -4 + 4 = 0

subtracting eq (4) from (8) we get,

y₁ = -4 - 2 = -6

subtracting eq (1) from (7) we get,

y₂ = -4 + 6 = 2

Therefore (10, -6) , (-4, 2) and (-2, 0) are the vertices of triangle.

Answer 2

Answer: co-ordinate of A(10,-6)

co-ordinate of B (-4,2)

co-ordinate of C (-2,0)

Step-by-step explanation:

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