Segment YW is an altitude of triangle XYZ. Find the area of the triangle. Triangle XYZ with altitude YW is shown. Point X is at 5, negative 3. Point Y is at 8, negative 1. Point Z is at 5, 4. Point W is at 5, negative 1. 7.5 9.5 10.5 15

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;

Where

(x₁, y₁) = (5, -3)

(x₂, y₂) = (5, 4)

Therefore, we have;

= 7

The length of segment YW is also given as follows;

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.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1