The coordinates of the vertices of a triangle are A(1,3), B(6,10), and C(11,18). Find the perimeter of the triangle when the coordinates are multiplied by 3.

Triangle IJK has the coordinates listed :



I (5 , -8) J (10 , -8) K (7 , 4)



Where is J' after a reflection over the y-axis?

The distance between A and B can be calculated using the distance formula:

distance(A,B)=sqrt((xb-xa)^2+(yb-ya)^2)
=sqrt((1-6)^2+(3-10)^2)
=sqrt(25+49)
=sqrt(74)
=8.602 approx.
You can find similarly the distances BC and CA.

Add up the sum AB+BC+CA which is the perimeter of the original triangle.
For the triangle with coordinates 3 times shown, multiply the original perimeter by 3.

To find the perimeter of a triangle, we need to calculate the sum of the lengths of its three sides.

Step 1: Find the lengths of the sides of the original triangle.
We can use the distance formula to find the length of each side of the triangle. The distance formula is given by:
Distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

For side AB:
x1 = 1, y1 = 3 (coordinates of A)
x2 = 6, y2 = 10 (coordinates of B)
Length AB = sqrt[(6 - 1)^2 + (10 - 3)^2]

For side BC:
x1 = 6, y1 = 10 (coordinates of B)
x2 = 11, y2 = 18 (coordinates of C)
Length BC = sqrt[(11 - 6)^2 + (18 - 10)^2]

For side AC:
x1 = 1, y1 = 3 (coordinates of A)
x2 = 11, y2 = 18 (coordinates of C)
Length AC = sqrt[(11 - 1)^2 + (18 - 3)^2]

Step 2: Multiply the coordinates by 3.
To find the coordinates of the vertices when they are multiplied by 3, we simply multiply the x-coordinates and y-coordinates by 3 for each vertex.

Coordinates of A when multiplied by 3: (1 * 3, 3 * 3) = (3,9)
Coordinates of B when multiplied by 3: (6 * 3, 10 * 3) = (18,30)
Coordinates of C when multiplied by 3: (11 * 3, 18 * 3) = (33,54)

Step 3: Find the lengths of the sides of the scaled triangle.
Now that we have the new coordinates, we can use the distance formula again to find the lengths of the sides of the scaled triangle using the same process as in Step 1.

For the scaled triangle with vertices A'(3,9), B'(18,30), and C'(33,54), repeat the distance formula calculations to find the lengths of sides A'B', B'C', and A'C'.

Step 4: Calculate the perimeter of the scaled triangle.
Add the lengths of the three sides of the scaled triangle to find its perimeter. Perimeter = Length A'B' + Length B'C' + Length A'C'.

By following these steps, you will be able to find the perimeter of the triangle when the coordinates are multiplied by 3.