Question

in a right triangle, the slopes of the two legs are 0 and undefined. what type of triangle is this? a. equilateral triangle b. scalene triangle c. isosceles triangle d. right triangle a quadrilateral has vertices at a(1,2), b(4,5), c(7,2), and d(4, - 1). which sides are perpendicular? a. none of the sides are perpendicular b. ab and bc c. bc and cd d. ab and ad which pair of points would create a line with a slope of 0? a. (3,4) and (3,7) b. (1,1) and (2,2) c. (1,1) and (1,2) d. (2,3) and (5,3)

Explanation:

Step1: Recall slope - triangle relationship

A slope of 0 means a horizontal line and an undefined slope means a vertical line. A triangle with a horizontal and a vertical side is a right - triangle.

Step2: Recall slope formula for quadrilateral

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For $A(1,2)$ and $B(4,5)$, $m_{AB}=\frac{5 - 2}{4 - 1}=1$. For $B(4,5)$ and $C(7,2)$, $m_{BC}=\frac{2 - 5}{7 - 4}=-1$. Since $m_{AB}\times m_{BC}=1\times(-1)= - 1$, $AB$ and $BC$ are perpendicular.

Step3: Recall slope formula for points

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $(x_1,y_1)$ and $(x_2,y_2)$, if $y_1 = y_2$, then $m = 0$. For the points $(2,3)$ and $(5,3)$, $m=\frac{3 - 3}{5 - 2}=0$.

Answer:

d. Right triangle
b. $AB$ and $BC$
d. $(2,3)$ and $(5,3)$