System of congruences, modular arithmetic
System of congruences, modular arithmetic

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25. The graph below shows two congruent triangles ABC and A’B’C’.
B
Which rigid motion would map ABC onto A’B’C’? (1) rotation of 90 degrees counterclockwise about the origin (2) translation of three units to the left and three units up (3) rotation of 180 degrees about the origin (4) reflection over the line y = x.

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01:08

Use Theorem 1.4 .3 to determine whether the graph has symmetries about the $x$ -axis, the $y$ axis, or the origin.(a) $x=5 y^{2}+9$(b) $x^{2}-2 y^{2}=3$(c) $x y=5$

05:14

Draw the rotation image of each triangle by reflecting the triangles in the given lines. State the coordinates of the rotation image and the angle of rotation.$\triangle T U V$ with vertices $T(0,4), U(2,3),$ and $V(1,2),$ reflected in the $y$ -axis and then the $x$ -axis

03:34

The point $(4,1)$ undergoes the following three successive transformations(A) Reflection about the line $y=x-1$(B) Translation through a distance 1 unit along the positive $x$-axis(C) Rotation through an angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction. Then, the coordinates of the final point are(A) $(4,3)$(B) $\left(\frac{7}{2}, \frac{7}{2}\right)$(C) $(0,3 \sqrt{2})$(D) $(3,4)$

04:57

Let $R_{l}$ be a reflection in the line $y=x$ and $R_{y}$ be a reflection in the $y$ -axis. Draw a grid and label the origin $O$.a. Plot the point $P(5,2)$ and its image $Q$ under the mapping $R_{y} \circ R_{l}$b. According to Theorem $14-8, m \angle P O Q=\underline{?}$c. Use the slopes of $\overline{O P}$ and $\overline{O Q}$ to verify that $\overline{O P} \perp \overline{O Q}$.d. Find the images of $(x, y)$ under $R_{y} \circ R_{l}$ and $R_{l} \circ R_{y}$

Transcript

we need to determine which of the following is um makes triangle abc become triangle A. Prime B. Prime C. Prime. So this is not a translation because if we move B. Up, it has to be below A not above A. So it’s not a translation. A rotation about the origin. So a. 12345 52. And then the new A. Is 12 And 12345.…