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प्रश्न
If area of triangle is 35 square units with vertices (2, −6), (5, 4), and (k, 4), then k is ______.
पर्याय
12
-2
−12, −2
12, −2
उत्तर
If area of triangle is 35 square units with vertices (2, −6), (5, 4), and (k, 4). Then k is 12, −2.
Explanation:
Given, the vertices of the triangle are (2, -6), (5, 4) and (k, 4);
`Delta` Area of = `Delta = 1/2 abs ((x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1))`
x1 = 2, y1 = 6, x2 = 5, y2 = 4, x3 = k, y3 = 4
`Delta` Area of `pm 35`
`pm 35 = 1/2 [2(4 - 4) + 6(5 - k) + k (120 - 4 k)`
`=> pm 35 = 1/2 [ 2 xx 0 + 6(5 - k) + 1 (20 - 4 k)]`
`=> pm 70 = 6(5 - k) + 20 - 4 k`
`=> pm 70 = 30 - 6 k + 20 - 4 k`
`=> pm 70 = 50 - 10 k`
`=> pm 70 = 5 - k`
7 = 5 - k
⇒ k = 5 - 7
k = -2
-7 = 5 - k
⇒ - 12 = - k
⇒ k = 12
अत: k = 12, -2
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