New
New
Year 10
Higher

Shapes on coordinate grids

I can calculate perimeter and area of shapes on coordinate grids.

New
New
Year 10
Higher

Shapes on coordinate grids

I can calculate perimeter and area of shapes on coordinate grids.

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Lesson details

Key learning points

  1. Shapes on coordinate grids do not often have their measurements clearly written.
  2. Instead, you are expect to calculate the desired lengths.
  3. This may involve Pythagoras' theorem, shape properties or equations of lines for example.

Keywords

  • Equation of a straight line - An equation of a line is any equation whose graph forms a straight line. These equations can be written in the form y = mx + c.

Common misconception

"The graphs of two straight line equations should always intersect at integer points on a coordinate grid."

The location with which the graphs of two straight line equations intersect can be found by simultaneously solving the pair of equations. The graphs of two straight line equations can intersect at either integer or non-integer values.

For some sets of straight line graphs there may be more than one visible "bounded polygon". Unless explicitly stated to the contrary, always assume the bounded polygon that will be focused on is the one whose sides are made from all the straight lines on the coordinate grid, not a subset of them.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
Choose the pair of coordinates that is the midpoint of the line segment AB.
An image in a quiz
(5, 3)
Correct answer: (7, 3)
(7, 7)
(3, 7)
4
Q2.
The pair of coordinates that is the midpoint of the line segment CD are .
An image in a quiz
Correct Answer: (2.5, 9), (2.5,9), (5/2, 9), (5/2,9)
Q3.
Which of these calculations finds the gradient of the line segment AB?
An image in a quiz
$${4+1}\over{10+5}$$
$${10+4}\over{5+1}$$
$${10-4}\over{5-1}$$
$${5+1}\over{10+4}$$
Correct answer: $${5-1}\over{10-4}$$
Q4.
The gradient of the line segment CD is to 3 decimal places.
An image in a quiz
Correct Answer: -0.222
Q5.
The length of the hypotenuse of this triangle is cm to 2 decimal places.
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Correct Answer: 26.25, 26.25cm, 26.25 cm
Q6.
Find the perimeter of this triangle. Give your answer in metres, correct to the nearest metre.
An image in a quiz
Correct Answer: 2 m, 2 metres, 2, 2m

6 Questions

Q1.
To find the length of the line segment CD you need to use theorem.
An image in a quiz
Correct Answer: Pythagoras' , Pythagoras, Pythagoras's
Q2.
The perimeter of trapezium ABCD is units (to 1 decimal place).
An image in a quiz
Correct Answer: 31.2, 31.2 units, 31.2units
Q3.
Match each measurement to its value.
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Correct Answer:length of line segment EF,7.07 units (2 d.p.)

7.07 units (2 d.p.)

Correct Answer:length of line segment FG,15 units

15 units

Correct Answer:length of line segment GH,3 units

3 units

Correct Answer:length of line segment HI,6.32 units (2 d.p.)

6.32 units (2 d.p.)

Correct Answer:length of line segment IE,4 units

4 units

Correct Answer:perimeter of pentagon EFGHI,35.4 units (1 d.p.)

35.4 units (1 d.p.)

Q4.
Match each shape to its area.
An image in a quiz
Correct Answer:area of rectangle JONM,50 units²

50 units²

Correct Answer:area of triangle JMK,10 units²

10 units²

Correct Answer:area of triangle KNL,6 units²

6 units²

Correct Answer:area of triangle JOL,15 units²

15 units²

Correct Answer:area of triangle JKL,19 units²

19 units²

Q5.
The area of triangle QPR is units².
An image in a quiz
Correct Answer: 21.5, 21.5 units², 21.5units²
Q6.
Calculate the area of the triangle bound by the three straight lines with equations: $$y=2$$, $$y=x$$, $$x+y=12$$. The area is units².
Correct Answer: 16, 16 units², 16units²