Question

homework for 3.1.4
3 - 46 juan bobo is resizing an image of a coqui for a presentation.
what is preserved (remains the same) about the pre - image
and the new image?
why is the new image not a rigid transformation?
3 - 47 the perimeter of the triangle at right is 52 units.
write and solve an equation based on the information in the diagram.
use your solution for x to calculate the length of each side of the triangle.
be sure to confirm that your answer is correct.
3 - 48 write the equation of each line described below:
a. a line that goes through
the points $(-7,10)$ and
$(1,4)$.
b. a line with a slope of $-\frac{3}{4}$
that passes through the
point $(-14,4)$.
c. a line with a slope of 0
that passes through the
point $(6, - 11)$.

Explanation:

Step1: Write the perimeter equation

The perimeter of a triangle is the sum of its sides. So, \((7x - 4)+19+(10x + 3)=52\).

Step2: Simplify the left - hand side

Combine like terms: \((7x+10x)+(-4 + 19+3)=52\), which simplifies to \(17x+18 = 52\).

Step3: Solve for \(x\)

Subtract 18 from both sides: \(17x=52 - 18\), so \(17x=34\). Then divide both sides by 17: \(x=\frac{34}{17}=2\).

Step4: Calculate the side lengths

For the side \(7x - 4\): Substitute \(x = 2\), \(7\times2-4=14 - 4 = 10\).
For the side \(19\) (it remains \(19\)).
For the side \(10x + 3\): Substitute \(x = 2\), \(10\times2+3=20 + 3=23\).

Step5: Confirm the answer

Check the perimeter: \(10 + 19+23=52\).

Answer:

\(x = 2\), the side lengths are \(10\), \(19\), and \(23\) units.