Question

day 7a check in
which type of transformation is pictured below?
show how you know!
image of coordinate plane with two triangles
a) translation: 5 units left and 1 unit up
b) translation: 1 unit left and 1 unit up
c) translation: 2 units right and 3 units down
d) reflection across x = 3
another image of coordinate plane with two triangles
a) rotation 90° counterclockwise about the origin
b) translation: 4 units left and 1 unit down
c) reflection across y = -2
d) translation: 1 unit left and 1 unit up
success criteria
i can determine which shape is the preimage and which is the image.
i can identify the transformation that occurred (translation, reflection, rotation, dilation)
i can explain how i know the transformation that occurred.
i can explain why the transformation that occurred is not the other three types.
mastery level
name

Explanation:

Step1: Analyze the first problem

• For the first transformation (triangle \(H'I'J'\) to \(HIJ\)):
• Let's assume a point - say, if we consider the movement of a vertex. A translation is a slide. If we count the units of horizontal and vertical movement.
• If we move from the pre - image to the image in the first case, we observe that it is a translation of \(5\) units right (opposite of left in option A) and \(1\) unit down (opposite of up in option A). But if we consider the movement from \(HIJ\) (assuming it as pre - image) to \(H'I'J'\) (image), we count the horizontal and vertical displacements.
• A reflection across \(x = 3\) (option D) would have a mirror - like property with respect to the line \(x=3\), but the figure does not show such a mirror - image property.
• For a translation: If we consider the change in \(x\) and \(y\) coordinates. Let's assume a general point \((x,y)\) in the pre - image. If the transformation is \(x\to x - 5\) (5 units left) and \(y\to y+1\) (1 unit up).

Step2: Analyze the second problem

• For the second transformation (triangle \(KLM\) to \(K'L'M'\)):
• A rotation of \(90^{\circ}\) counter - clockwise about the origin (option A) would change the orientation of the triangle in a specific rotational way (using the rotation formula \((x,y)\to(-y,x)\)), but the orientation of the two triangles does not match the rotational property.
• A reflection across \(y=-2\) (option C) would have a mirror - like symmetry with respect to the line \(y =- 2\), which is not observed.
• For a translation: If we consider the movement of vertices. If we assume a vertex of \(\triangle KLM\) and its corresponding vertex in \(\triangle K'L'M'\), we can count the horizontal and vertical displacements. A translation of \(4\) units left (change in \(x\) coordinate: \(x\to x - 4\)) and \(1\) unit up (change in \(y\) coordinate: \(y\to y + 1\)) does not match. But if we consider the movement from \(\triangle KLM\) (pre - image) to \(\triangle K'L'M'\) (image) as a translation of \(1\) unit left (\(x\to x-1\)) and \(1\) unit up (\(y\to y + 1\))

Answer:

For the first problem: A. translation: \(5\) units left and \(1\) unit up
For the second problem: D. translation: \(1\) unit left and \(1\) unit up