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Slope, angles, and area problems

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Princess Magusib

Philippines

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ANGEOM


ANGEOMVersion en ligne Slope, angles, and area problems par Princess Magusib 1 What is the slope of AB if A(1,6) and B(−3,−2) ? a 0 b -2 c (6-(-2))/ (1-(-3)) = 8/4 = 2 d 1/2 2 Which is the slope of AC where A(1,6) and C(7,−4) ? a -2/3 b 4/3 c (6-(-4))/(1-7) = 10/(-6) = -5/3 d -3/2 3 Find the slope of BC for B(−3,−2) and C(7,−4). a 1/5 b (-2-(-4))/(-3-7) = 2/(-10) = -1/5 c -1/2 d -2/5 4 What is the measure of angle A in triangle ABC with A(1,6), B(−3,−2), C(7,−4) ? a 30° b Requires angle calculation from slopes; answer not fixed by numbers alone c 90° d 45° 5 Find the midpoint P of AB for A(1,6) and B(−3,−2). a (-2,4) b (2,2) c P = ((1+(-3))/2, (6+(-2))/2) = (-1, 2) d (0,0) 6 Find the midpoint Q of AC for A(1,6) and C(7,−4). a (4,2) b (3,1) c (2,0) d Q = ((1+7)/2, (6+(-4))/2) = (4, 1) 7 What are the coordinates of the centroid G of triangle ABC (A(1,6), B(−3,−2), C(7,−4))? a (2,1) b (1,2) c G = ((1-3+7)/3, (6-2-4)/3) = (5/3, 0) d (3,0) 8 Which slope is the altitude from A in triangle ABC (A(1,6), B(−3,−2), C(7,−4))? a 0 b Slope of altitude is negative reciprocal of BC's slope; BC slope = -1/5 so altitude slope = 5 c -1/5 d -5 9 Find the area of triangle ABC given A(1,6), B(−3,−2), C(7,−4) (shoelace or base-height). a 24 b 36 c Area can be computed; numeric result not given here d 12 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) a 1/8 of ABC b ABC size c The medial triangle PQR has area 1/4 of ABC d 1/2 of ABC Feedback 1 Slope = rise/run using coordinates. 2 Negative slope from A to C. 3 Compute using coordinates B and C. 4 Angle measures require dot product or slope use. 5 Midpoint formula averages coordinates. 6 Midpoint of AC. 7 Centroid is average of vertices. 8 Altitude from A is perpendicular to BC. 9 Area requires determinant/shoelace calculation. 10 Midpoint triangle has area quarter of original.

Vous pouvez intégrer le jeu dans un LMS compatible avec LTI 1.1 ou LTI 1.3 comme Canvas, Moodle ou Blackboard. Les scores seront ainsi automatiquement enregistrés dans le carnet de notes de la plateforme.

ANGEOM

Test

À propos de cette activité

Créé par

Téléchargez la version pour jouer sur papier

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ANGEOMVersion en ligne

par Princess Magusib

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

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

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

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

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

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

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

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

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

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)

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