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Home
SAT
Math Section
Geometry and Trigonometry

Set - 2

Premium Content

Chief Editor

Mar 27, 2024

0

Table of Contents

$$x^{2}+20x+y^{2}+16y=-20$<br/><br/>The equation above defines a circle in the $xy$-plane. What are the coordinates of the center of the circle?$
$A rectangle has an area of 63 square meters and a length of 9 meters. What is the width, in meters, of the rectangle?$
$What is the diameter of the circle in the $xy$-plane with equation $\left(x-5\right)^{2}+\left(y-3\right)^{2}=16$?$
$Triangle $XYZ$ is similar to triangle $RSI$' such that $X$, $Y$, and $Z$ correspond to $R$, $S$, and $T$, respectively. The measure of $\angle Z$ is $20^{*}$ and $2XY=RS$. What is the measure of $\angle T$?$
$Triangle $ABC$ is similar to triangle $XYZ$, such that $A$, $B$, and $C$ correspond to $X$, $Y$, and $Z$ respectively. The length of each side of triangle $XYZ$ is $2$ times the length of its corresponding side in triangle $ABC$. The measure of side $AB$ is $16$. What is the measure of side $XY$?<br/><br/>### $14$<br/><br/>### $16$$
$In $\bigtriangleup\bm{XYZ}$, the measure of $\bigtriangleup\bm{X}$ is 23${}^{*}$ and the measure of $\bigtriangleup\bm{Y}$ is 66${}^{*}$ What is the measure of $\bigtriangleup\bm{ZZ}$?$
$A circle in the $xy$-plane has its center at $(-4,-6)$. Line $k$ is tangent to this circle at the point $(-7,-7)$. What is the slope of line $k$?$
$A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the optimal number of containers to be displayed on a shelf. Which of the following expresses the volume, $V$, in cubic inches, of such containers, where $r$ is the radius, in inches?$
$Quadrilateral $P^{\prime}Q^{\prime}R^{\prime}S^{\prime}$ is similar to quadrilateral $PQRS$, where $P$, $Q$, $R$, and $S$ correspond to $P^{\prime}$, $Q^{\prime}$, $R^{\prime}$, and $S^{\prime}$, respectively. The measure of angle $P$ is $30^{\circ}$, the measure of angle $Q$ is $50^{\circ}$, and the measure of angle $R$ is $70^{\circ}$. The length of each side of $P^{\prime}Q^{\prime}R^{\prime}S^{\prime}$ is 3 times the length of each corresponding side of $PQRS$. What is the measure of angle $P^{\prime}$?$
$In triangle $ABC$, the measure of angle $A$ is $50^{\circ}$. If triangle $ABC$ is isosceles, which of the following is NOT a possible measure of angle $B$ ?$

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$x^{2}+20x+y^{2}+16y=-20$The equation above defines a circle in the $xy$-plane. What are the coordinates of the center of the circle?

Difficulty: Hard

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A:

$(-20,-16)$

B:

$(-10,-8)$

C:

$(10,8)$

D:

$(20,16)$

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