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Question 8
The points (-4,0), (4,0) and (0,3) are the vertices of a
(A) Right angled triangle
(B) Isosceles triangle
(C) Equilateral triangle
(D) Scalene triangle

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Solution

Let A(-4,0), B(4,0) and C(0,3) are the given vertices.
Now, distance between A(-4,0) and B(4,0),
Distance between two points (x1,y1) and (x2,y2)
D=(x2x1)2+(y2y1)2
AB=[4(4)]2+(00)2]
=(4+4)2=82=8
Distance between B(4,0) and C(0,3),
BC=(04)2+(30)2=16+9=25=5
Distance between A(-4,0) and C(0,3),
AC=[0(4)]2+(30)2=16+9=25=5
BC=AC
Hence, ΔABC is an isosceles triangle because an isosceles triangle has two sides equal.

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