Question

From the information given below find which of the point is between the other two. If the points are not collinear, state so. d(X, Y) = 15, d(Y, Z) = 7, d(X, Z) = 8​

Answer 1

akshithapadidam avatar

akshithapadidam

14.07.2020

Math

Secondary School

answered

From the information given below, find which of the point is between the other two. Ifthe points are not collinear ,state so. d(R,S)=8 , d(S,T)=6 , d(R,T)=4. Answer this question correctly I will thanks your 3 Answers and I will mark you as brainliest

2

SEE ANSWERS

Unlocked badge showing an astronaut’s boot touching down on the moon

See what the community says and unlock a badge.

Answer

4.0/5

33

harshpatel98105

Ace

205 answers

53.2K people helped

Answer:

For any three-distinct collinear points P, Q and R, the point Q is said to be in between P and R if

d (P, Q) + d (Q, R) = d (P, R).

(i) Given: d (P, R) = 7, d (P, Q) = 10, d (Q, R) = 3

Now, consider d (P, Q) = 10 ……….(I)

And d (P, R) + d (Q, R) = 7 + 3 = 10 ……….(II)

∴ Using (I) and (II), we have

d (P, R) + d (Q, R) = d (P, Q)

⇒ R lies between P and Q.

(ii) Given: d (R, S) = 8, d (S, T) = 6, d (R, T) = 4

Here, d (R, S) + d (S, T) = 8 + 6 = 14 ≠ 4 = d (R, T)

Also, d (R, S) + d (R, T) = 8 + 4 = 12 ≠ 6 = d (S, T)

And d (S, T) + d (R, T) = 6 + 4 = 10 ≠ 8 = d (R, S)

Hence, the points R, S and T are non-collinear.

(iii) Given: d (A, B) = 16, d (C, A) = 9, d (B, C) = 7

Now, consider d (A, B) = 16 ……….(I)

And d (C, A) + d (B, C) = 9 + 7 = 16 ……….(II)

∴ Using (I) and (II), we have

d (C, A) + d (B, C) = d (A, B)

⇒ C lies between A and B.

(iv) Given: d (L, M) = 11, d (M, N) = 12, d (N, L) = 8

Here, d (L, M) + d (M, N) = 11 + 12 = 23 ≠ 8 = d (N, L)

Also, d (L, M) + d (N, L) = 11 + 8 = 19 ≠ 12 = d (M, N)

And d (M, N) + d (N, L) = 12 + 8 = 20 ≠ 11= d (L, M)

Hence, the points L, M and N are non-collinear.

(v) Given: d (X, Y) = 15, d (Y, Z) = 7, d (X, Z) = 8

Now, consider d (X, Y) = 15 ……….(I)

And d (Y, Z) + d (X, Z) = 7 + 8 = 15 ……….(II)

∴ Using (I) and (II), we have

d (Y, Z) + d (X, Z) = d (X, Y)

⇒ Z lies between X and Y.

(vi) Given: d (D, E) = 5, d (E, F) = 8, d (D, F) = 6

Here, d (D, E) + d (E, F) = 5 + 8 = 13 ≠ 6 = d (D, F)

Also, d (D, E) + d (D, F) = 5 + 6 = 11 ≠ 8 = d (E, F)

And d (E, F) + d (D, F) = 8 + 6 = 14 ≠ 5 = d (D, E)

Hence, the points D, E and F are non-collinear.

Answer 2

Check whether the points are collinear

d(X, Y) = 15 d(Y, Z) = 7 d(X, Z) = 8

d(X, Y) is the maximum among the given distances.

d(X, Y) = d(Y, Z) + d(X, Z)

15 = 7 + 8

15 = 15

LHS = RHS