Question

if the coordinates of the mid point of the sides of a triangle ABC are (1,1),(2,-3),(3,4).find the coordinates of the vertices​

Answer 1

Answer:

coordinates of triangles are let :a (1,1),b (2,-3)andc (3,4)...

then centroid=(x1+x2+x3)/3 and (y1+y2+y3)/3

=(1+2+3)/3, (1-3+4)/3

=6/3,-6/3

=2,-2

Step-by-step explanation:

Answer 2

Answer:

A(x1, y1) = (2, 8)

B(x2, y2) = (-4, -6)

C(x3, y3) = (4, 0)

Step-by-step explanation:

Let the midpoints of sides AB, BC and AC be P, Q and R respectively.

Let co ordinates of A be x1, y1

B be x2, y2

C be x3, y3

By midpont formula (x=x1+x2/2 ,

y=y1+y2/2)

•P(1,1)

1 = (x1 + x2)/2

so, x1 + x2 = 2×1

so, x1 + x2 = 2 ......(1)

1 = (y1 + y2) / 2

so, y1 + y2 = 2 × 1

so, y1 + y2 = 2 ......(2)

•Q(2, -3)

2 = (x2 + x3) / 2

so, x2 + x3 = 2×3

so, x2 + x3 = 6 .......(3)

-3 = (y2 + y3) / 2

so, y2 + y3 = 2*-3

so, y2 + y3 = -6 .......(4)

•R(3, 4)

3 = (x3 + x1) / 2

so, x3 + x1 = 3*2

so, x3 +x1 = 6 ......(5)

4 = (y3 + y1) / 2

so, y3 + y1 = 2*4

so, y3 + y1 = 8 ......(6)

Adding (1), (2) and (3)...

x1+x2+x2+x3+x3+x1 = 2+4+6

so, 2(x1+x2+x3) = 12

so, x1 + x2 + x3 = 12/2

so, x1 + x2 +x3 = 6 ....(7)

Adding (4), (5) and (6)...

y1 + y2 + y2 + y3 + y3 + y1 = 2 + (-6) + 8

so, 2(y1 + y2 + y3) = 4

so, y1 + y2 + y3 = 4/2

so, y1 + y2 + y3 = 2 .....(8)

Substituing (1) in (7)...

x1 + x2 + x3 = 6

so, 2 + x3 = 6

so, x3 = 6 - 2

so, x3 = 4 ...(9)

Substituing (2) in (7)...

x1 + x2 + x3 = 6

so, x1 + 4 = 6

so, x1 = 6 - 4

so, x1 = 2 .... (10)

Substituting (9) and (10) in (7)

x2 + 4 + 6 = 6

so, x2 = 6 - 6 - 4

so, x2 = -4 .....(11)

Similarly

Substituting (4) in (8)....

y1 + y2 + y3 = 2

so, 2 + y3 = 2

so, y3 = 2 - 2

so, y3 = 0 ....(12)

Substituting (5) in (8).....

y1 + y2 + y3 = 2

so, y1 + (-6) = 2

so, y1 = 2 + 6

so, y1 = 8 .....(13)

Substituting (12) and (13) in (8)..

y1 + y2 + y3 = 2

so, 8 + y2 + 0 = 2

so, y2 = 2 - 8

so, y2 = -6 ......(14)

From (9), (10), (11), (12), (13) and (14).....

A(x1, y1) = (2, 8)

B(x2, y2) = (-4, -6)

C(x3, y3) = (4, 0)

Hope it helps...

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