Question

The co-ordinate of the vertices of triangle abc are a(7,2) ,b(9,10) and c(1,4) .If e and f are the mid-points of ab and ac respectively ,prove that ef=1/2bc.

Answer 1

Answer:

Given:

A (7,2) , B (9,10) , C (1,4)

Let point E ( x1, y1) & F ( x2, y2)

Coordinates of point E = ((9+7)/2, (10+2)/2)

Coordinates of point E = (8, 6)

[ By midpoint Formula]

Coordinates of point F = ((7+1)/2, (2+4)/2)

Coordinates of point F = (4, 3)

[ By midpoint Formula]

Length of EF = √(8-4)² + (6-3)²

[ By distance formula, √(x1-x2)² + (y1-y2)²]

= √ 4² + 3²

= √ 16 + 9

= √25

Length of EF = 5 units………..(1)

Length of BC = √(9 - 1)² + (10 -4)²

[ By distance formula, √(x1-x2)² + (y1-y2)²]

= √ 8² + 6²

= √ 64 + 36

= √100

Length of BC = 10 units………….(2)

From eq 1 and 2

EF = ½ BC

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