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प्रश्न
Without using the distance formula, show that the points A(4, −2), B(−4, 4) and C(10, 6) are the vertices of a right-angled triangle.
उत्तर
The given points are A(4, −2), B(−4, 4) and C(10, 6).
Slope of AB = `(4 + 2)/(-4 - 4)`
Slope of AB = `6/(-8)`
Slope of AB = `(-3)/4` ...(1)
Slope of BC = `(6 - 4)/(10 + 4)`
Slope of BC = `2/14`
Slope of BC = `1/7` ...(2)
Slope of AC = `(6 + 2)/(10 - 4)`
Slope of AC = `8/6`
Slope of AC = `4/3` ...(3)
From (1) and (3)
It can be seen that:
Slope of AB = `(-1)/"Slope of AC"`
Hence, AB ⊥ AC
Thus, the given points are the vertices of a right-angled triangle.
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