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In VYX, the centroid is Z. Use the diagram to solve the problems.

7. If XR=24, find XZ and ZR.
8. If XZ = 44, find XR and ZR.
9. If VZ=14, find VP and ZP.
10. If VP=51, find VZ and ZP.
11. If ZO 10, find YZ and YO.
12. If YO= 18, find YZ and ZO.

User Courtland
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1 Answer

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To solve for XZ and ZR when XR=24, XZ=16 and ZR=8. To solve for XR and ZR when XZ=44, XR=132 and ZR=44. To solve for VP and ZP when VZ=14, VP=9.33 and ZP=4.67. To solve for VZ and ZP when VP=51, VZ=153 and ZP=17. To solve for YZ and YO when ZO=10, YZ=6.67 and YO=3.33. To solve for YZ and ZO when YO=18, YZ=54 and ZO=6.

To solve for XZ and ZR when XR=24:

Since the centroid is Z, the distance from X to Z is two-thirds of XR. Therefore, XZ is equal to (2/3) * 24 = 16.

The distance from Z to R is one-third of XR. Therefore, ZR is equal to (1/3) * 24 = 8.

To solve for XR and ZR when XZ=44:

Since the centroid is Z, the distance from X to Z is three times XZ. Therefore, XR is equal to 3 * 44 = 132.

The distance from Z to R is one-third of XR. Therefore, ZR is equal to (1/3) * 132 = 44.

To solve for VP and ZP when VZ=14:

Since the centroid is Z, the distance from V to Z is two-thirds of VZ. Therefore, VP is equal to (2/3) * 14 = 9.33.

The distance from Z to P is one-third of VZ. Therefore, ZP is equal to (1/3) * 14 = 4.67.

To solve for VZ and ZP when VP=51:

Since the centroid is Z, the distance from V to Z is three times VP. Therefore, VZ is equal to 3 * 51 = 153.

The distance from Z to P is one-third of VP. Therefore, ZP is equal to (1/3) * 51 = 17.

To solve for YZ and YO when ZO=10:

Since the centroid is Z, the distance from Y to Z is two-thirds of YZ. Therefore, YZ is equal to (2/3) * 10 = 6.67.

The distance from Y to O is one-third of ZO. Therefore, YO is equal to (1/3) * 10 = 3.33.

To solve for YZ and ZO when YO=18:

Since the centroid is Z, the distance from Y to Z is three times YO. Therefore, YZ is equal to 3 * 18 = 54.

The distance from Z to O is one-third of YO. Therefore, ZO is equal to (1/3) * 18 = 6.

User CTABUYO
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