Question

The coordinates of the vertices of ∆ABC are A(7, 2) ,B(9,10) and C(1, 4). If A and F are the midpoints of AB and AC respectively,Prove that EF=½ BC.
(Class 10 Maths Sample Question Paper)

Answer 1

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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