Photo AI
Triangle T is drawn on a coordinate grid - OCR - GCSE Maths - Question 18 - 2023 - Paper 1
Question 18
Triangle T is drawn on a coordinate grid. (a) Triangle A is translated by \(\left( \frac{6}{3} \right)\) to give triangle T. Draw and label triangle A on the grid. ... show full transcript
Worked Solution & Example Answer:Triangle T is drawn on a coordinate grid - OCR - GCSE Maths - Question 18 - 2023 - Paper 1
Step 1
Triangle A is translated by \(\left( \frac{6}{3} \right)\) to give triangle T.
Answer
To find the vertices of triangle A from triangle T, we need to reverse the translation. Triangle T's coordinates can be represented as ((x_T, y_T)). To find triangle A's vertices, we will subtract the translation components:
- For the x-coordinate: (x_A = x_T - 2)
- For the y-coordinate: (y_A = y_T - 0)
Assuming T is located at (2, 1), the coordinates for triangle A will be (0, 1). Thus, draw triangle A with vertices that reflect this position.
Step 2
Triangle T is rotated through 90° anticlockwise about (0, 0) to give triangle B.
Answer
To rotate a point ((x, y)) 90° anticlockwise about the origin, the new coordinates are given by the transformation: ((x', y') = (-y, x))
Applying this to the coordinates of triangle T, you will calculate the new coordinates for triangle B. For instance, if triangle T's vertex is at (2, 1), the new vertex for triangle B after rotation will be (-1, 2). Draw triangle B at these new coordinates.
Step 3
Triangle T is reflected in the line \(y = -1\) to give triangle C.
Answer
To reflect a point across the line (y = -1), you take the distance from the point to the line and then place the reflected point the same distance on the opposite side. For a point ((x, y)):
- Determine the vertical distance from (y) to -1: (d = y + 1)
- The reflected y-coordinate will be (y' = -1 - d = -1 - (y + 1) = -y - 2)
For example, reflecting (2, 1) will yield the new point (2, -3). Draw triangle C using the newly reflected vertices.