Question

. A(-1, 3), B(-1, x) and C(4, 3) are the vertices of ∆ ABC,
m angle B = 90 using distance formula
As soon as possible

Answer 1

Step-by-step explanation:

given B = 90°

using Pythagoras theorem:

AB² + BC² = AC²

AB² = (x + 1)² + (-1 -3)² = x² + 2x + 1 + 16 = x² + 2x + 17

BC² = (3-x)² + (4+1)² = 9 - 6x + x² +25= x² -6x +34

AC² = (3-3)² + (4+1)² = 25

.

.

x² + 2x + 17 + x² - 6x +34 = 25

2x² - 4x + 51 = 25

2x² - 4x + 26 = 0

x² - 2x + 13 = 0

(x)² - 2(x)(1) + (1)² - 1 + 13 = 0

(x - 1)² + 12 =0

(x - 1)² = -12

which is not possible, hence the triangle is not right angled triangle.

Answer 2

Step-by-step explanation:

given B = 90°

using Pythagoras theorem:

AB² + BC² = AC2

AB² = (x + 1)²+(-1 -3)² = x² + 2x + 1+16= x²+2x+

17

BC² = (3-x)² + (4+1)² = 9 - 6x + x² +25= x²-6x +34 AC² = (3-3)² + (4+1)² = 25

x² + 2x +17 + x²-6x +34 = 25

2x² - 4x + 51 = 25

2x²-4x+26=0

x² -2x+13=0

(x)² - 2(x)(1) + (1)² - 1 + 13 = 0

(x-1)²+12=0

(x-1)²=-12

which is not possible, hence the triangle is not right angled triangle.