Enlargement and scale factors

Your learning journey

Enlarge shapes from a stated centre, including positive fractional factors, and explain how centre and factor determine the image.

Follow the task-specific calculator guidance in Apply. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.

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Ready.

Connect & Check

Centre: fixed point from which displacements are scaled. Scale factor k: multiplier of directed distances from the centre. Similar: same shape, with corresponding lengths proportional.

Share

In pairs, predict the first step and compare your reasons before reading the worked solution: D1 Model: centre origin, k=2 sends (2,1) to (4,2). Enlarge (3,2) by k=3 about origin.

Present

For centre C and point P, the image lies k times as far along the ray CP for positive k. In coordinates P′=C+k(P−C). Subtract the centre, multiply the displacement, then add the centre back. A factor between 0 and 1 makes the image smaller; k=1 leaves it unchanged.

Draw rays from the centre through vertices. Multiply each centre-to-vertex distance by k; join images in order. Check a side-length ratio and one ray. The centre remains fixed.

Apply

Optional check: for C(1,1), P(2,3), k=2, calculate 1+2×(2−1) and 1+2×(3−1). Expect 3 and 5. Brackets preserve the displacement calculation.

Apply and extend

Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.

Recall & Review

Retrieval without notes

Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.

Not checked.

Independent exit evidence

P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.

Recall & Review and prepare

A bearing is measured clockwise from north at the starting point and written using three digits. Scale drawings convert real distances to paper lengths using a consistent scale.

Retrieve F1 again in one week. Bring your working and one question.

Higher alternative: Negative scale factors

Higher route: replace the 2-minute A3 feedback and the two 4-minute Challenge discussions with this 10-minute taught extension. Retain core P1–P2. Set HX1–HX2 as the final four minutes of that alternative, and use the shared challenges later if needed. The core route remains 60 minutes; the extension is not an additional compulsory ten minutes. Route choice reflects tier curriculum, not temporary support needs.

A negative factor puts the image on the opposite side of the centre. For centre C(1,1), point P(3,2) and factor −2, the displacement P−C=(2,1). Multiply by −2 to get (−4,−2), then add C: P′=(−3,−1). The distance from C doubles; the direction reverses. Use each vertex separately and check a side-length ratio of 2.

HX1–HX2: teacher review. Completion is not mastery.