The vertices of a triangle are A(8, -24), B(8, -8), and C(16, -8). If the triangle is dilated by a scale factor of
1
4
what will be the coordinates of C’ ?
To find the coordinates of C' after the triangle has been dilated by a scale factor of 1/4, we need to follow these steps:
Step 1: Find the center of dilation.
To find the center of dilation, we can choose any point on the triangle. Let's take point B(8, -8) as the center of dilation.
Step 2: Find the distance from the center of dilation to point C.
Using the distance formula, we can calculate the distance between B(8, -8) and C(16, -8):
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((16 - 8)^2 + (-8 - (-8))^2)
d = √((8)^2 + (0)^2)
d = √(64 + 0)
d = √64
d = 8
Step 3: Apply the scale factor.
Since the scale factor is 1/4, we need to multiply the distance (d) by 1/4 to get the new distance (d') after dilation:
d' = d * (1/4)
d' = 8 * (1/4)
d' = 8/4
d' = 2
Step 4: Find the coordinates of C'.
To find the coordinates of C', we need to move 2 units from the center of dilation (B) in the direction of C. Since C is to the right of B, we move 2 units to the right:
x-coordinate of C' = 8 + 2 = 10
y-coordinate of C' = -8
Therefore, the coordinates of C' after the triangle is dilated by a scale factor of 1/4 will be C'(10, -8).
assuming the dilation is centered at (0,0) then just multiply all the numbers by 1/4
oh, and learn to type fractions!