Please help me find x
1 answer:
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Question:
A translation is applied to the triangle where A(1, 4) , B(2, -2) , and C(-3, 2). The image is the triangle that has vertices A′(5, 4) , B′(6, -2) , and C′(1, 2).
Answer:
Step-by-step explanation:
Given
From the translation of triangle ABC to A'B'C',
It will be observed that the y coordinates of both triangle remain unchanged.
This implies that triangle ABC is translated on the x coordinates alone.
Considering the x coordinates of A and A', we have:
Make k the subject
When 4 is added to the x coordinates of B and C, it gives the x coordinates of B' and C'.
Hence, the rule of translation is:
Answer:
Option B.
Step-by-step explanation:
The given curve is
We need to find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve .
Let the vertex in quadrant I be (x,y), then the vertex in quadrant II is (-x,y) .
Length of the rectangle = 2x
Width of the rectangle = y
Area of a rectangle is
Substitute the value of y from the given equation.
.... (1)
Differentiate with respect to x.
Equate , to find the critical points.
Divide both sides by 6.
The value of x can not be negative because side length can not be negative.
Substitute x=3 in equation (1).
The area of the largest rectangle is 108 square units.
Therefore, the correct option is B.