Respuesta :
Answer:
The correct option is;
10.5
Step-by-step explanation:
The given coordinates are;
Triangle XYZ
Coordinates of X = (5, -3)
Coordinates of Y = (8, -1)
Coordinates of Z = (5, 4)
Coordinates of point W = (5, -1)
Given that W is on segment XZ, we have;
Length of segment XZ = A base of the triangle is given by the relation;
[tex]Length \ of \ segment = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where
(x₁, y₁) = (5, -3)
(x₂, y₂) = (5, 4)
Therefore, we have;
[tex]Length \ of \ XZ= \sqrt{\left (4-(-3) \right )^{2}+\left (5-5 \right )^{2}}[/tex] = 7
The length of segment YW is also given as follows;
[tex]Length \ of \ YW= \sqrt{\left (-1-(-1) \right )^{2}+\left (5-8 \right )^{2}} = 3[/tex]
Given that the height of the triangle XYZ is given by segment YW, the area of triangle XYZ = 1/2 × Base × Height = 1/2×7×3 = 21/2 = 10.5
The area of triangle XYZ = 10.5.
