The points (3, 0) , (, −2) and (4, −1) are vertices of triangle right angled at vertex . Find the value of . pls give explanation also !!!!
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If the points A (3,0), B (a,-2), and C (4,-1) are the vertices of a triangle ABC right angled at vertex A, what is the value of a?
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5 Answers

Hungenahalli Sitaramarao Badarinath, Ph.D. in Civil Engineering. Maths keeps one mentally active.
Answered July 26, 2017
The coordinates of A (3,0), B (a,-2) and C (4,-1) are the vertices of a RAT with the right angle at A. What is a?
Since ABC is a RAT, AC^2 + AB^2 = BC^2.
AC^2 = [(4–3)^2+(-1–0)^2] = [1+1] = 2
AB^2 = [(a-3)^2 +(-2–0)^2] = (a-3)^2+4
BC^2= [(4-a)^2 +(-1+2)^2] = (4-a)^2+1
AC^2 + AB^2 = BC^2, or
2 + (a-3)^2+4 = (4-a)^2+1, or
2 + a^2 - 6a + 9 + 4 = 16 - 8a + a^2 + 1, or
8a - 6a =16+1–2–9–4, or
2a = 17–15 = 2, or
a=1.
Check: AC^2 = 2. AB^2 = 8. BC^2 = 3^2+1 = 10.
AC^2 + AB^2 = BC^2, or
2+8=10. Correct.
Hence a = 1.
Step-by-step explanation:
hope it helps you