Find the equations of the medians of ΔABC whose vertices are A(–1, 2), B(2, 1) and C(0, 4). Hence, find the co-ordinates of the centroid of ΔABC.
Straight Line Eq
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Question

Find the equations of the medians of ΔABC whose vertices are A(–1, 2), B(2, 1) and C(0, 4). Hence, find the co-ordinates of the centroid of ΔABC.

KnowledgeBoat · Accepted Answer

By using Midpoint formula, (x, y) = D (Midpoint of BC): B(2, 1)and C(0, 4) D = E (Midpoint of AC): A(-1, 2) and C(0, 4) E = F (Midpoint of AB): A(-1, 2) and B(2, 1) F = Median AD through A(-1, 2) and By slope formula: Substitute values we get: The equation of the line will be given by two-point form i.e., y - y1 = m(x - x1) Substituting values in above equation we get, ⇒ y - 2 = (x + 4) ⇒ 4(y - 2) = (x + 1) ⇒ 4y - 8 = x + 1 ⇒ x - 4y + 9 = 0 Median BE through B(2, 1) and The equation of the line will be given by two-point form i.e., ⇒ y - 1 = (x - 2) ⇒ 5(y - 1) = 4(x - 2) ⇒ 5y - 5 = 4x - 8 ⇒ 4x + 5y - 13 = 0 Median CF through C(0, 4) and Since C(0, 4) is the y-intercept, we use y = mx + c: ⇒ y = -5x + 4 ⇒ 5x + y - 4 = 0 By using centroid formula, Using A(-1, 2), B(2, 1), and C(0, 4): Hence, equations of medians are x - 4y + 9 = 0, 4x + 5y - 13 = 0 and 5x + y - 4 = 0, coordinates of centroid .

Mathematics

Find the equations of the medians of ΔABC whose vertices are A(–1, 2), B(2, 1) and C(0, 4). Hence, find the co-ordinates of the centroid of ΔABC.

Straight Line Eq

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Mathematics

Find the equations of the medians of ΔABC whose vertices are A(–1, 2), B(2, 1) and C(0, 4). Hence, find the co-ordinates of the centroid of ΔABC.

Straight Line Eq

Related Questions

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M and N are two points on the x-axis and y-axis respectively. P(3, 2) divides the line segment MN in the ratio 2 : 3. Find :
(i) the co-ordinates of M and N
(ii) slope of the line MN

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