Question

In Triangle ARP, centroid E is on median AX¯¯¯¯¯¯¯¯ . AE = y+6 and EX = 3y-2. Find AX (1 point) Responses 73 7 thirds 11 11 512 5 and 1 half 13

Answer 1

To find AX, we can use the properties of a centroid in a triangle. The centroid is the point where all three medians intersect, and it divides each median into a ratio of 2:1.

Since AE represents 2 parts and EX represents 1 part, we can set up the following equation:

(AE / EX) = 2/1

Substituting the given values, we have:

(y + 6) / (3y - 2) = 2/1

Cross-multiplying, we get:

(y + 6) = 2(3y - 2)
y + 6 = 6y - 4
4 + 4 = 6y - y
8 = 5y
y = 8/5

Now that we have the value of y, we can find AX by substituting it into the expression:

AE = y + 6
AE = 8/5 + 6
AE = 8/5 + 30/5
AE = 38/5

Since AX is two times AE, we have:

AX = 2 * (38/5)
AX = 76/5

Therefore, the value of AX is 76/5, which can be simplified to 15 1/5.