The coordinates of the vertices of △XYZ are X(−5, 5), Y(−3, −2), and Z(4, 0). The slope of XZ is , the slope of YZ is , and the slope of XY is . △XYZ a right triangle because ____________.

-7/2 -5/9 -2/7 2/7 9/5 is is not no two of these slopes have a product of -1 two of these problems have a product of -1

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abidemiokin abidemiokin · Answer 1 · 2021-01-16T01:39:07+01:00

Answer:

Slope of XZ = -5/9

Slope of YZ = 2/7

Slope of XY = -7/2

Step-by-step explanation:

Slope is expressed as;

m = y2-y1/x2-x1

For XZ

X(−5, 5), and Z(4, 0)

Slope of XZ = 0-5/4-(-5)

Slope of XZ = -5/4+5

Slope of XZ = -5/9

For YZ

Y(−3, −2), and Z(4, 0).

Slope of YZ = 0-(-2)/4-(-3)

Slope of YZ = 2/4+3

Slope of YZ = 2/7

For XY

X(−5, 5), Y(−3, −2)

Slope of XY = -2-5/-3-(-5)

Slope of XY = -7/-3+5

Slope of XY = -7/2

For two lines to be perpendicular, the product of their slope must be -1

Taking the product of XY and YZ

mXY * mYZ = -7/2 * 2/7

mXY * mYZ = -1

since the product of mXY and mYZ is -1. this shows that line XY is perpendicular to YZ and showing that the triangle XYZ is right triangle