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3 years ago

What are the coordinates of the circumcenter of a triangle with vertices A(−3,−4), B(1,−4), and C(−3,0)?

Mathematics

2 answers:

ra1l [238]3 years ago

8 0

The coordinate of the circumecenter of a triangle is A

kvv77 [185]3 years ago

6 0

The circumcenter is equal distance from all 3 verices.
Using distance formula, equate distance to A with distance to C:
$(x+3)^2 +(y+4)^2 = (x+3)^2 + y^2$
The x terms cancel, Expand and solve for y:
$y^2 +8y+16 = y^2$
$y = -2$
Now do same thing for point A and B:
$(x+3)^2 + (y+4)^2 = (x-1)^2 + (y+4)^2$
y terms cancel
$x^2 +6x+9 = x^2-2x+1$
$x = -1$

Circumcenter is the point (-1,-2)

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3 years ago

Just Need A Few Questions Answered To Finish My Quiz, Any Help Would Be Much Appreciated.

kvv77 [185]

Given the triangle

PQR

with points

P(8,0)

Q(6,2)

R(-2,-4)

And the triangle

P'Q'R'

with points

P'(4,0)

Q'(3,1)

R'(-1,-2)

Part A. Scale factor

Using the vertex

P( 8, 0)

P'(4,0)

the dilatation factor is given by

$\frac{4}{8}=\frac{1}{2}$

The triangle has a dilatation factor of 1/2

Part B:

P''Q''R'' after using P'Q'R' reflected about the y axis

to make a reflection over the y axis

coordinates (x,y) turn into coordinates (-x,y)

as follows

$P^{\prime}(4,0)\rightarrow P^{\prime\prime}(-4,0)$ $Q^{\prime}(3,1)\rightarrow Q^{\prime\prime}(-3,1)$ $R^{\prime}(-1,-2)\rightarrow R^{\prime\prime}(1,-2)$

Then triangle P''Q''R'' has coordinates

P''(-4,0)

Q''(-3,1)

R''(1,-2)

Part C:

PQR is congruent to P''Q''R''?

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

Then the triangles are not congruent