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Transforming a shape involves changing the size and/or the location of the shape.
- The rule that will take the triangle to a congruent triangle is
- The rule that will take the triangle to a figure that is similar is
.
- The rule that will take the triangle to a figure that is not similar or congruent is
.
When a shape is transformed by a rigid transformation, then the image of the shape will be congruent to the original shape.
An example of a rigid transformation is a reflection over the x-axis; and the rule is:
So, a rule that will take the triangle to a congruent triangle is
When a shape is transformed by a nonrigid transformation, then the image of the shape will not be congruent to the original shape, however the original shape and the transformed shape would be similar
An example of a nonrigid transformation is a dilation by a scale factor od 0.5; and the rule is:
So, a rule that will take the triangle to a figure that is similar is
However, if the x and y coordinates of the shape are dilated by different scale factors, then the resulting shape would neither be similar nor be congruent to the original shape.
A rule that will take the triangle to a figure that is not similar or congruent is .
Read more about transformation at:
Answer:
k = - , k = 2
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
The condition for equal roots is b² - 4ac = 0
Given
kx² + 2x + k = - kx ( add kx to both sides )
kx² + 2x + kx + k = 0 , that is
kx² + (2 + k)x + k = 0 ← in standard form
with a = k, b = 2 + k and c = k , thus
(2 + k)² - 4k² = 0 ← expand and simplify left side
4 + 4k + k² - 4k² = 0
- 3k² + 4k + 4 = 0 ( multiply through by - 1 )
3k² - 4k - 4 = 0 ← in standard form
(3k + 2)(k - 2) = 0 ← in factored form
Equate each factor to zero and solve for k
3k + 2 = 0 ⇒ 3k = - 2 ⇒ k = -
k - 2 = 0 ⇒ k = 2