lovetaya.blogg.se - Triangle reflection on y axis

Recall that, for a general point 𝑃 ( 𝑥, 𝑦 ), a reflection in the 𝑥 - a x i s maps

Is the measure of angle 𝐴 𝐵 𝐶 less than, greater than, or equal to the measure of angle 𝐴 ′ 𝐵 ′ 𝐶 ′?.

Determine the coordinates of 𝐴 ′, 𝐵 ′, and 𝐶 ′.

Three points 𝐴, 𝐵, and 𝐶 with coordinates ( 1, 3 ), ( 1, 2 ), and ( 4, 1 ), respectively,Īre reflected in the 𝑥 - a x i s to the points 𝐴 ′, 𝐵 ′, and 𝐶 ′. Plotting the above image points and connecting them in the correct order, we get the image of the quadrilateral shown in the diagram below.Įxample 3: Solving a Problem about Points Reflected in the 𝑥-Axis The 𝑦 - a x i s, with each vertex of the image at the same perpendicular distance from the 𝑦 - a x i s as the corresponding vertex of Remember that a reflection in the 𝑦 - a x i s takes a geometric figure and maps it to its congruent mirror image on the opposite side of Observe that vertex 𝐴 has an 𝑥-coordinate of 8 and a 𝑦-coordinate of 6, so it can be written as the point

The coordinates of the corresponding image points. We can then use the above transformation to work out Here, our first step is to read off the coordinates of the vertices of the quadrilateral. This means it maps point 𝑃 onto the image point 𝑃 ′ by changing the sign of the 𝑥-coordinate Recall that, for a general point 𝑃 ( 𝑥, 𝑦 ), a reflection in the 𝑦 - a x i s maps Next, we shall examine reflection in the 𝑦 - a x i s, which follows a very similar pattern to reflection in the 𝑥 - a x i s. We conclude that the pair of triangles 𝐴 and 𝐵 represent a reflection in the 𝑥 - a x i s. Triangle 𝐵, we would have found that the image points were the vertices of triangle 𝐴. Moreover, if we had started with the vertices of It is easy to check that these image points are precisely the vertices shown for triangle 𝐵. Using the fact that 𝑃 ( 𝑥, 𝑦 ) → 𝑃 ′ ( 𝑥, − 𝑦 ), we find the image points as follows: Reading off from the diagram, we see that triangle 𝐴 has vertices with coordinates ( − 3, 5 ), ( − 2, 2 ), and ( − 5, 3 ). Although this should be obvious from the diagram, we will use the definition of a reflection in

However, as there is no such triangle, then 𝐶 has not been reflected in the 𝑥 - a x i s, so the reflected triangles must be