0:00
Coordinates Part 3: Shapes
Select the skills to practice, and then click Go!
Identifying shapes from coordinates
Identifying axis-aligned rectangles
\[ (1,1), (4,1), (4,3), (1,3) \]
Decide if four coordinate points form a rectangle.
Identifying squares from coordinates
\[ (0,0), (2,0), (2,2), (0,2) \]
Decide if four coordinate points form a square.
Fourth vertex problems – with diagrams
Fourth vertex of axis-aligned rectangle
\[ \text{Find D: } (?, ?) \]
Find the missing vertex of an axis-aligned rectangle.
Fourth vertex of axis-aligned square
\[ \text{Find S: } (?, ?) \]
Find the missing vertex of an axis-aligned square.
Fourth vertex of parallelogram
\[ \vec{AB} = \vec{DC} \]
Find the fourth vertex using vector properties.
Fourth vertex of tilted rectangle
\[ \text{Non-axis-aligned} \]
Find the fourth vertex when rectangle is tilted.
Fourth vertex problems – no diagrams
Fourth vertex of rectangle (no diagram)
\[ A(1,2), B(4,2), C(4,5) \]
Find missing vertex from coordinates only.
Fourth vertex of square (no diagram)
\[ P(0,0), Q(3,0), R(3,3) \]
Find missing vertex from coordinates only.
Fourth vertex of parallelogram (no diagram)
\[ \vec{AB} = \vec{DC} \]
Find missing vertex using vectors.
Fourth vertex of tilted rectangle (no diagram)
\[ \text{Non-axis-aligned} \]
Find missing vertex of tilted rectangle.
Perimeter and area
Perimeter of axis-aligned rectangle
\[ P = 2(l + w) \]
Calculate perimeter using coordinate differences.
Perimeter with Pythagorean sides
\[ 3 + 4 + 5 = 12 \]
Calculate perimeter including a diagonal side.
Perimeter involving surds
\[ P = 4\sqrt{5} \]
Calculate perimeter when sides involve surds.
Area of axis-aligned rectangle
\[ A = l \times w \]
Calculate area using coordinate differences.
Area of right-angled triangle
\[ A = \frac{1}{2}bh \]
Calculate area of right triangle with horizontal base.
Area of triangle (any base)
\[ A = \frac{1}{2} \times 4 \times 3 \]
Calculate area with horizontal or vertical base.
Verification skills
Verify a rectangle
\[ \text{Show ABCD is a rectangle} \]
Verify by checking properties.
Verify a parallelogram
\[ \vec{PQ} = \vec{SR} \]
Verify by checking parallel sides.
Verify a square
\[ \text{Is ABCD a square?} \]
Verify whether four points form a square.
Verify a rhombus
\[ EF = FG = GH = HE \]
Verify whether four points form a rhombus.
Timer (Optional)
0:00
Question