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Slope, angles, and area problems

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Philippines

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Slope, angles, and area problems

by Princess Magusib
1

What is the slope of AB if A(1,6) and B(−3,−2) ?

2

Which is the slope of AC where A(1,6) and C(7,−4) ?

3

Find the slope of BC for B(−3,−2) and C(7,−4).

4

What is the measure of angle A in triangle ABC with A(1,6), B(−3,−2), C(7,−4) ?

5

Find the midpoint P of AB for A(1,6) and B(−3,−2).

6

Find the midpoint Q of AC for A(1,6) and C(7,−4).

7

What are the coordinates of the centroid G of triangle ABC (A(1,6), B(−3,−2), C(7,−4))?

8

Which slope is the altitude from A in triangle ABC (A(1,6), B(−3,−2), C(7,−4))?

9

Find the area of triangle ABC given A(1,6), B(−3,−2), C(7,−4) (shoelace or base-height).

10

If P is the midpoint of AB and Q is the midpoint of AC, what is area of triangle PQR relative to ABC? (R is midpoint of BC)

Feedback

Slope = rise/run using coordinates.

Negative slope from A to C.

Compute using coordinates B and C.

Angle measures require dot product or slope use.

Midpoint formula averages coordinates.

Midpoint of AC.

Centroid is average of vertices.

Altitude from A is perpendicular to BC.

Area requires determinant/shoelace calculation.

Midpoint triangle has area quarter of original.

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