Section 12 - Geometry (Edition 1)

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Category 68 Example 1 - no calculation required

Match the square of the given radius and the given coordinates of the center with the equations in the answer choices.

Category 68 Example 2 Step 1 - mental math

The midpoint of the two points can be determined using mental math.

Category 68 Example 3 - mental math

After simplifying the equation, the remaining calculation can be done using mental math.

Half of coefficient of x is -2 and half of coefficient of y is 7. These are the factors.

Square of radius is -2 squared + 7 squared + number on right side of the equation.

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Category 71 Example 1 - mental math

Since the hypotenuse has root 2 term, the triangle is a 45-45-90 triangle. Based on the side ratios for 45-45-90 triangle, the base and the length of the triangle are the value of a = 6.

The area can be determined using mental math: 6 times 6 divided by 2 is 36/2=18.

Category 71 Example 3 - mental math

The two sides 8 and 10 are the ratio of Pythagorean triple 6:8:10. Hence, the third side = height must be 6.

The area can be determined using mental math: 8 times 6 divided by 2 is 48/2 = 24.

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Category 72 Example 2 - mental math

The sides AB and DE are corresponding sides of two similar triangles. Since AB is one-fourth of DE, BC will be one-fourth of the corresponding side CE = 32/4 =8.

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Category 73 Example 1 - mental math

Since the diagonal is 6 root 2, the side is 6. Area is 6 squared = 36.